Volume 87 Number 314 November 2018

VOLUME 87 NUMBER 314 NOVEMBER 2018

AMERICANMATHEMATICALSOCIETY

EDITED BY Daniele Boffi Susanne C. Brenner, Managing Editor Martin Burger Albert Cohen Ronald F. A. Cools Bruno Despres Qiang Du Bettina Eick Howard C. Elman Ivan Graham Ralf Hiptmair Mark van Hoeij Frances Kuo Sven Leyffer Christian Lubich Gunter Malle Andrei Mart´ınez-Finkelshtein James McKee Michael J. Mossinghoff Michael J. Neilan Fabio Nobile Adam M. Oberman Frank-Olaf Schreyer Christoph Schwab Zuowei Shen Igor E. Shparlinski Chi-Wang Shu Andrew V. Sutherland Daniel B. Szyld Hans Volkmer Barbara Wohlmuth Mathematics of Computation This journal is devoted to research articles of the highest quality in computational mathematics. Areas covered include numerical analysis, computational discrete mathematics, including number theory, algebra and combinatorics, and related fields such as stochastic numerical methods. Articles must be of significant computational interest and contain original and substantial mathematical analysis or development of computational methodology. Submission information. See Information for Authors at the end of this issue. PublicationontheAMSwebsite.Articles are published on the AMS website individually after proof is returned from authors and before appearing in an issue. Subscription information. Mathematics of Computation is published bimonthly and is also accessible electronically from www.ams.org/journals/. Subscription prices for Volume 87 (2018) are as follows: for paper delivery, US$779.00 list, US$623.20 institutional member, US$701.10 corporate member, US$467.40 individual member; for electronic delivery, US$686.00 list, US$548.80 institutional member, US$617.40 corporate member, US$411.60 individual member. Upon request, subscribers to paper delivery of this journal are also entitled to receive electronic delivery. If ordering the paper version, add US$6 for delivery within the United States; US$36 for delivery outside the United States. Subscription renewals are subject to late fees. See www.ams.org/help-faq for more journal subscription information. Back number information. For back issues see the www.ams.org/backvols. Subscriptions and orders should be addressed to the American Mathematical Society, P.O. Box 845904, Boston, MA 02284-5904 USA. All orders must be accompanied by pay- ment. Other correspondence should be addressed to 201 Charles Street, Providence, RI 02904-2213 USA. Copying and reprinting. Individual readers of this publication, and nonprofit libraries act- ing for them, are permitted to make fair use of the material, such as to copy an article for use in teaching or research. Permission is granted to quote brief passages from this publication in reviews, provided the customary acknowledgment of the source is given. Republication, systematic copying, or multiple reproduction of any material in this publication is permitted only under license from the American Mathematical Society. Requests for permission to reuse portions of AMS publication content are handled by the Copyright Clearance Center. For more information, please visit www.ams.org/publications/pubpermissions. Excluded from these provisions is material for which the author holds copyright. In such cases, requests for permission to reuse or reprint material should be addressed directly to the author(s). Copyright ownership is indicated in the notice in the lower right-hand corner of the first page of each article.

Mathematics of Computation (ISSN 0025-5718 (print); ISSN 1088-6842 (online)) is published bimonthly by the American Mathematical Society at 201 Charles Street, Providence, RI 02904- 2213 USA. Periodicals postage is paid at Providence, Rhode Island. Postmaster: Send address changes to Mathematics of Computation, American Mathematical Society, 201 Charles Street, Providence, RI 02904-2213 USA. c 2018 by the American Mathematical Society. All rights reserved. This journal is indexed in Mathematical Reviews, Zentralblatt MATH, Science Citation Index , Science Citation IndexTM–Expanded, ISI Alerting ServicesSM, CompuMath Citation Index ,andCurrent Contents/Physical, Chemical & Earth Sciences. This journal is archived in Portico and in CLOCKSS. ∞ The paper used in this book is acid-free and falls within the guidelines established to ensure permanence and durability. 10987654321 232221201918 MATHEMATICS OF COMPUTATION CONTENTS Vol. 87, No. 314 November 2018

Léna¨ıcChizat, Gabriel Peyré,Bernhard Schmitzer, and Fran¸cois- Xavier Vialard, Scaling algorithms for unbalanced optimal transport problems ...... 2563 Christian Kreuzer and Emmanuil H. Georgoulis, Convergence of adaptive discontinuous Galerkin methods ...... 2611 Paul Houston and Thomas P. Wihler, An hp-adaptive Newton- discontinuous-Galerkin finite element approach for semilinear elliptic boundary value problems ...... 2641 Andrea Cangiani, Emmanuil H. Georgoulis, and Younis A. Sabawi, Adaptive discontinuous Galerkin methods for elliptic interface problems 2675 Jeonghun J. Lee and Ragnar Winther, Local coderivatives and approximation of Hodge Laplace problems ...... 2709 Siyang Wang, Anna Nissen, and Gunilla Kreiss, Convergence of finite difference methods for the wave equation in two space dimensions . . . . 2737 Ralf Kornhuber, Daniel Peterseim, and Harry Yserentant, An analysis of a class of variational multiscale methods based on subspace decomposition ...... 2765 Eliane´ Bécache, Patrick Joly, and Valentin Vinoles, On the analysis of perfectly matched layers for a class of dispersive media and application to negative index metamaterials ...... 2775 Dario A. Bini, Stefano Massei, and Beatrice Meini, Semi-infinite quasi- Toeplitz matrices with applications to QBD stochastic processes . . . . . 2811 Yang Zhou and Xiaojun Chen, Spherical t-designs for approximations on the sphere ...... 2831 Zhijian He, Quasi-Monte Carlo for discontinuous integrands with singularities along the boundary of the unit cube ...... 2857 Jared Duker Lichtman and Carl Pomerance, Improved error bounds for the Fermat primality test on random inputs ...... 2871 Andrew R. Booker, Finite connected components of the aliquot graph . . 2891 St˚alAanderaa, Lars Kristiansen, and Hans Kristian Ruud, Search for good examples of Hall’s conjecture ...... 2903 Markus Hittmeir, A babystep-giantstep method for faster deterministic integer factorization ...... 2915 Jonathan W. Sands and Brett A. Tangedal, Computing annihilators of class groups from derivatives of L-functions ...... 2937 Philip Brinkmann and Günter M. Ziegler, Small f-vectors of 3-spheres and of 4-polytopes ...... 2955 Frédéric Chyzak, Thomas Dreyfus, Philippe Dumas, and Marc Mezzarobba, Computing solutions of linear Mahler equations ...... 2977 Javier Cilleruelo, Florian Luca, and Lewis Baxter, Every positive integer is a sum of three palindromes ...... 3023 INDEX TO VOLUME 87 (2018)

Aanderaa, St˚al,Lars Kristiansen, and Hans Kristian Ruud. Search for good examples of Hall’s conjecture, 2903 Acosta, Gabriel, Juan Pablo Borthagaray, Oscar Bruno, and Mart´ınMaas. Regularity theory and high order numerical methods for the (1D)-fractional Laplacian, 1821 Altmann, R., and C. Zimmer. Runge-Kutta methods for linear semi-explicit operator differential- algebraic equations, 149 Angot, Philippe, and Rima Cheaytou. On the error estimates of the vector penalty-projection methods: Second-order scheme, 2159 Banjai, Lehel, and Alexander Rieder. Convolution quadrature for the wave equation with a nonlinear impedance boundary condition, 1783 Bao, Weizhu, and Chunmei Su. Uniform error bounds of a finite difference method for the Klein- Gordon-Zakharov system in the subsonic limit regime, 2133 Baumstark, Simon, Erwan Faou, and Katharina Schratz. Uniformly accurate exponential-type integrators for Klein-Gordon equations with asymptotic convergence to the classical NLS splitting, 1227 Baxter, Lewis. See Cilleruelo, Javier Bécache, Eliane,´ Patrick Joly, and Valentin Vinoles. On the analysis of perfectly matched layers for a class of dispersive media and application to negative index metamaterials, 2775 Bini, Dario A., Stefano Massei, and Beatrice Meini. Semi-infinite quasi-Toeplitz matrices with applications to QBD stochastic processes, 2811 Birgin, E. G., N. Krejić,and J. M. Mart´ınez. On the employment of inexact restoration for the minimization of functions whose evaluation is subject to errors, 1307 Booker, Andrew R. Finite connected components of the aliquot graph, 2891 Börm,Steffen. Adaptive compression of large vectors, 209 Borthagaray, Juan Pablo. See Acosta, Gabriel Bras-Amorós,Maria, and Julio Fernández-González. Computation of numerical semigroups by means of seeds, 2539 Bringmann, Bjoern, Daniel Cremers, Felix Krahmer, and Michael Moeller. The homotopy method revisited: Computing solution paths of `1-regularized problems, 2343 Brinkmann, Philip, and Günter M. Ziegler. Small f-vectors of 3-spheres and of 4-polytopes, 2955 Broersen, D., W. Dahmen, and R. P. Stevenson. On the stability of DPG formulations of transport equations, 1051 Brugiapaglia, Simone, Fabio Nobile, Stefano Micheletti, and Simona Perotto. A theoretical study of COmpRessed SolvING for advection-diffusion-reaction problems, 1 Bruin, Peter, and Andrea Ferraguti. On L-functions of quadratic Q-curves, 459 Bruno, Oscar. See Acosta, Gabriel Burgos Gil, JoséIgnacio, Ricardo Menares, and Juan Rivera-Letelier. On the essential minimum of Faltings’ height, 2425 Burman, Erik, and Peter Hansbo. Stabilized nonconforming finite element methods for data assimilation in incompressible flows, 1029 Burman, Erik, Peter Hansbo, and Mats G. Larson. A cut finite element method with boundary value correction, 633 Büthe,Jan. An analytic method for bounding ψ(x), 1991 Cai, Yongyong, and Jie Shen. Error estimates for a fully discretized scheme to a Cahn-Hilliard phase-field model for two-phase incompressible flows, 2057 Cai, Yongyong, and Yongjun Yuan. Uniform error estimates of the conservative finite difference method for the Zakharov system in the subsonic limit regime, 1191 Cangiani, Andrea, Emmanuil H. Georgoulis, and Younis A. Sabawi. Adaptive discontinuous Galerkin methods for elliptic interface problems, 2675 Charles, Zachary. Generating random factored ideals in number fields, 2047 Cheaytou, Rima. See Angot, Philippe Chen, Long, Jun Hu, and Xuehai Huang. Fast auxiliary space preconditioners for linear elasticity in mixed form, 1601 Chen, Xiaojun. See Zhou, Yang Chen, Zhangxin. See He, Ruijian Cheng, Wanyou, and Yu-Hong Dai. Gradient-based method with active set strategy for `1 optimization, 1283 INDEX TO VOLUME 87 (2018)

Chizat, Léna¨ıc,Gabriel Peyré,Bernhard Schmitzer, and Fran¸cois-Xavier Vialard. Scaling algorithms for unbalanced optimal transport problems, 2563 Chkifa, Abdellah, Nick Dexter, Hoang Tran, and Clayton G. Webster. Polynomial approximation via compressed sensing of high-dimensional functions on lower sets, 1415 Christiansen, Snorre H. On eigenmode approximation for Dirac equations: Differential forms and fractional Sobolev spaces, 547 Chyzak, Frédéric,Thomas Dreyfus, Philippe Dumas, and Marc Mezzarobba. Computing solutions of linear Mahler equations, 2977 Cilleruelo, Javier, Florian Luca, and Lewis Baxter. Every positive integer is a sum of three palindromes, 3023 Coquel, Frédéric,Shi Jin, Jian-Guo Liu, and Li Wang. Entropic sub-cell shock capturing schemes via Jin-Xin relaxation and Glimm front sampling for scalar conservation laws, 1083 Cravero, I., G. Puppo, M. Semplice, and G. Visconti. CWENO: Uniformly accurate reconstructions for balance laws, 1689 Cremers, Daniel. See Bringmann, Bjoern

Dabrowski,, Andrzej, and Lucjan Szymaszkiewicz. Orders of Tate-Shafarevich groups for the Neumann-Setzer type elliptic curves, 1509 Dahmen, W. See Broersen, D. Dai, Yu-Hong. See Cheng, Wanyou Daniels, Harris B., Alvaro´ Lozano-Robledo, Filip Najman, and Andrew V. Sutherland. Torsion subgroups of rational elliptic curves over the compositum of all cubic fields, 425 Detinko, A., D. L. Flannery, and A. Hulpke. Zariski density and computing in arithmetic groups, 967 Dexter, Nick. See Chkifa, Abdellah DiPasquale, Michael. Dimension of mixed splines on polytopal cells, 905 Dohrmann, Clark R. See Oh, Duk-Soon Dreyfus, Thomas. See Chyzak, Frédéric Drungilas, P., J. Jankauskas, and J. Siurys.ˇ On Littlewood and Newman polynomial multiples of Borwein polynomials, 1523 Dumas, Philippe. See Chyzak, Frédéric Efremenko, Klim, J. M. Landsberg, Hal Schenck, and Jerzy Weyman. The method of shifted partial derivatives cannot separate the permanent from the determinant, 2037 Elsey, Matt, and Selim Esedo¯glu. Threshold dynamics for anisotropic surface energies, 1721 Ervin, V. J., N. Heuer, and J. P. Roop. Regularity of the solution to 1-D fractional order diffusion equations, 2273 Esedo¯glu,Selim. See Elsey, Matt Faber, Laura, and Habiba Kadiri. Corrigendum to New bounds for ψ(x), 1451 Faou, Erwan. See Baumstark, Simon Feng, Ruyong. On the computation of the Galois group of linear difference equations, 941 Feng, Xinlong. See He, Ruijian Fernández-González,Julio. See Bras-Amorós,Maria Ferraguti, Andrea. See Bruin, Peter Flannery, D. L. See Detinko, A. Franz, Sebastian, and Gunar Matthies. A unified framework for time-dependent singularly perturbed problems with discontinuous Galerkin methods in time, 2113 Freitas, Pedro. Sharp bounds for the modulus and phase of Hankel functions with applications to Jaeger integrals, 289 Friedland, Shmuel, and Lek-Heng Lim. Nuclear norm of higher-order tensors, 1255 Fung, King Cheong, and Ben Kane. On sign changes of cusp forms and the halting of an algorithm to construct a supersingular elliptic curve with a given endomorphism ring, 501 Gallouët,T., R. Herbin, J.-C. Latché,and D. Maltese. Convergence of the MAC scheme for the compressible stationary Navier-Stokes equations, 1127 Gander, Martin J., and Soheil Hajian. Analysis of Schwarz methods for a hybridizable discontinuous Galerkin discretization: The many-subdomain case, 1635 Georgoulis, Emmanuil H. See Cangiani, Andrea . See Kreuzer, Christian Glaubitz, Jan, Philipp Offner,¨ and Thomas Sonar. Application of modal filtering to a spectral difference method, 175 INDEX TO VOLUME 87 (2018)

González-Jiménez,Enrique, and Alvaro´ Lozano-Robledo. On the torsion of rational elliptic curves over quartic fields, 1457 Grenié,Lo¨ıc,and Giuseppe Molteni. Explicit bounds for generators of the class group, 2483 Gulliver, T. Aaron. See Rebenich, Niko Guzmán,Johnny, and Maxim Olshanskii. Inf-sup stability of geometrically unfitted Stokes finite elements, 2091 Hadjimichael, Yiannis, and David I. Ketcheson. Strong-stability-preserving additive linear multistep methods, 2295 Hajian, Soheil. See Gander, Martin J. Han, Bin, Qingtang Jiang, Zuowei Shen, and Xiaosheng Zhuang. Symmetric canonical quincunx tight framelets with high vanishing moments and smoothness, 347 Hangelbroek, T., F. J. Narcowich, C. Rieger, and J. D. Ward. An inverse theorem for compact d Lipschitz regions in R using localized kernel bases, 1949 Hansbo, Peter. See Burman, Erik He, Ruijian, Xinlong Feng, and Zhangxin Chen. H1-Superconvergence of a difference finite element method based on the P1 − P1-conforming element on non-uniform meshes for the 3D Poisson equation, 1659 He, Zhijian. Quasi-Monte Carlo for discontinuous integrands with singularities along the boundary of the unit cube, 2857 Herbin, R. See Gallouët,T. Heuer, N. See Ervin, V. J. Hittmeir, Markus. A babystep-giantstep method for faster deterministic integer factorization, 2915 Hofmann, Bernd. See Plato, Robert Houston, Paul, and Thomas P. Wihler. An hp-adaptive Newton-discontinuous-Galerkin finite element approach for semilinear elliptic boundary value problems, 2641 Hu, Jun. See Chen, Long Huang, Weizhang, and Lennard Kamenski. On the mesh nonsingularity of the moving mesh PDE method, 1887 Huang, Xuehai. See Chen, Long Hulpke, A. See Detinko, A. Hurst, Greg. Computations of the Mertens function and improved bounds on the Mertens conjecture, 1013 Hutzenthaler, Martin, Arnulf Jentzen, and Xiaojie Wang. Exponential integrability properties of numerical approximation processes for nonlinear stochastic differential equations, 1353 Jankauskas, J. See Drungilas, P. Jeannerod, Claude-Pierre, and Siegfried M. Rump. On relative errors of floating-point operations: Optimal bounds and applications, 803 Jentzen, Arnulf. See Hutzenthaler, Martin Jiang, Qingtang. See Han, Bin Jiang, Shidong. See Zhang, Qian Jin, Shi. See Coquel, Frédéric Joly, Patrick. See Bécache, Eliane´ Ju, Lili, Xiao Li, Zhonghua Qiao, and Hui Zhang. Energy stability and error estimates of exponential time differencing schemes for the epitaxial growth model without slope selection, 1859 Kadiri, Habiba. See Faber, Laura Kamenski, Lennard. See Huang, Weizhang Kane, Ben. See Fung, King Cheong Kemper, Gregor, Ngo Viet Trung, and Nguyen Thi Van Anh. Toward a theory of monomial preorders, 2513 Ketcheson, David I. See Hadjimichael, Yiannis King, Oliver D., Cris Poor, Jerry Shurman, and David S. Yuen. Using Katsurada’s determination of the Eisenstein series to compute Siegel eigenforms, 879 Kokkala, Janne I., and Patric R. J. Osterg˚ard.¨ The chromatic number of the square of the 8-cube, 2551 Kornhuber, Ralf, Daniel Peterseim, and Harry Yserentant. An analysis of a class of variational multiscale methods based on subspace decomposition, 2765 INDEX TO VOLUME 87 (2018)

Krahmer, Felix. See Bringmann, Bjoern Kreiss, Gunilla. See Wang, Siyang Krejić,N. See Birgin, E. G. Krenn, Daniel, and Volker Ziegler. Non-minimality of the width-w non-adjacent form in conjunction with trace one τ-adic digit expansions and Koblitz curves in characteristic two, 821 Kreuzer, Christian, and Emmanuil H. Georgoulis. Convergence of adaptive discontinuous Galerkin methods, 2611 Kristiansen, Lars. See Aanderaa, St˚al Kublik, Catherine, and Richard Tsai. An extrapolative approach to integration over hypersurfaces in the level set framework, 2365 Kuszmaul, William. Fast algorithms for finding pattern avoiders and counting pattern occurrences in permutations, 987 Labrande, Hugo. Computing Jacobi’s theta in quasi-linear time, 1479 Landsberg, J. M. See Efremenko, Klim Larson, Mats G. See Burman, Erik Latché,J.-C. See Gallouët,T. Latché,J. C., and K. Saleh. A convergent staggered scheme for the variable density incompressible Navier-Stokes equations, 581 Lee, Jeonghun J., and Ragnar Winther. Local coderivatives and approximation of Hodge Laplace problems, 2709 Lee, Yoonjin, and Yoon Kyung Park. A continued fraction of order twelve as a modular function, 2011 Lehoucq, R. B., F. J. Narcowich, S. T. Rowe, and J. D. Ward. A meshless Galerkin method for non-local diffusion using localized kernel bases, 2233 Li, Hengguang. An anisotropic finite element method on polyhedral domains: Interpolation error analysis, 1567 Li, Xiao. See Ju, Lili Lichtman, Jared Duker, and Carl Pomerance. Improved error bounds for the Fermat primality test on random inputs, 2871 Lim, Lek-Heng. See Friedland, Shmuel Linke, A., C. Merdon, M. Neilan, and F. Neumann. Quasi-optimality of a pressure-robust nonconforming finite element method for the Stokes-problem, 1543 Liu, Hailiang, and Hairui Wen. Error estimates for the AEDG method to one-dimensional linear convection-diffusion equations, 123 Liu, Jian-Guo. See Coquel, Frédéric Liu, Jian-Guo, Li Wang, and Zhennan Zhou. Positivity-preserving and asymptotic preserving method for 2D Keller-Segal equations, 1165 Lopez, L., and S. Maset. Time-transformations for the event location in discontinuous ODEs, 2321 Lozano-Robledo, Alvaro.´ See Daniels, Harris B. . See González-Jiménez, Enrique Lu, Jianfeng, and Zhennan Zhou. Frozen Gaussian approximation with surface hopping for mixed quantum-classical dynamics: A mathematical justification of fewest switches surface hopping algorithms, 2189 Luca, Florian. See Cilleruelo, Javier Ma, Yunyun, and Yuesheng Xu. Computing highly oscillatory integrals, 309 Maas, Mart´ın. See Acosta, Gabriel Maltese, D. See Gallouët,T. Mart´ınez,J. M. See Birgin, E. G. Mart´ınez-Finkelshtein, A., A. Sri Ranga, and D. O. Veronese. Extreme zeros in a sequence of para-orthogonal polynomials and bounds for the support of the measure, 261 Mascot, Nicolas. Certification of modular Galois representations, 381 Maset, S. See Lopez, L. Massei, Stefano. See Bini, Dario A. Mathé,Peter. See Plato, Robert Matthies, Gunar. See Franz, Sebastian Meini, Beatrice. See Bini, Dario A. INDEX TO VOLUME 87 (2018)

Melman, A. Eigenvalue bounds for matrix polynomials in generalized bases, 1935 Menares, Ricardo. See Burgos Gil, JoséIgnacio Merdon, C. See Linke, A. Mezzarobba, Marc. See Chyzak, Frédéric Micheletti, Stefano. See Brugiapaglia, Simone Moeller, Michael. See Bringmann, Bjoern Molteni, Giuseppe. See Grenié,Lo¨ıc Morini, Benedetta, Margherita Porcelli, and Philippe L. Toint. Approximate norm descent methods for constrained nonlinear systems, 1327 Mustapha, Kassem. FEM for time-fractional diffusion equations, novel optimal error analyses, 2259 Najman, Filip. See Daniels, Harris B. Narcowich, F. J. See Hangelbroek, T. . See Lehoucq, R. B. Neilan, M. See Linke, A. Neumann, F. See Linke, A. Neville, Stephen. See Rebenich, Niko Nissen, Anna. See Wang, Siyang Nobile, Fabio. See Brugiapaglia, Simone Nogneng, Dorian, and Eric´ Schost. On the evaluation of some sparse polynomials, 893 Offner,¨ Philipp. See Glaubitz, Jan Oh, Duk-Soon, Olof B. Widlund, Stefano Zampini, and Clark R. Dohrmann. BDDC Algorithms with deluxe scaling and adaptive selection of primal constraints for Raviart-Thomas vector fields, 659 Olshanskii, Maxim. See Guzmán,Johnny Olver, Sheehan. See Townsend, Alex Osterg˚ard,Patric¨ R. J. See Kokkala, Janne I. Park, Yoon Kyung. See Lee, Yoonjin Perotto, Simona. See Brugiapaglia, Simone Peterseim, Daniel. See Kornhuber, Ralf Peyré,Gabriel. See Chizat, Léna¨ıc Plato, Robert, Peter Mathé,and Bernd Hofmann. Optimal rates for Lavrentiev regularization with adjoint source conditions, 785 Pomerance, Carl. See Lichtman, Jared Duker Poor, Cris. See King, Oliver D. Porcelli, Margherita. See Morini, Benedetta Puppo, G. See Cravero, I. Qiao, Zhonghua. See Ju, Lili Qiu, Weifeng, Jiguang Shen, and Ke Shi. An HDG method for linear elasticity with strong symmetric stresses, 69 Ramming, Tobias, and Holger Wendland. A kernel-based discretisation method for first order partial differential equations, 1757 Ranga, A. Sri. See Mart´ınez-Finkelshtein, A. Rebenich, Niko, T. Aaron Gulliver, Stephen Neville, and Ulrich Speidel. An analog of the prime number theorem for finite fields via truncated polylogarithm expansions, 855 Rieder, Alexander. See Banjai, Lehel Rieger, C. See Hangelbroek, T. Rivera-Letelier, Juan. See Burgos Gil, JoséIgnacio Roop, J. P. See Ervin, V. J. Rowe, S. T. See Lehoucq, R. B. Rump, Siegfried M. See Jeannerod, Claude-Pierre Ruud, Hans Kristian. See Aanderaa, St˚al Sabawi, Younis A. See Cangiani, Andrea Saleh, K. See Latché,J. C. Sands, Jonathan W., and Brett A. Tangedal. Computing annihilators of class groups from derivatives of L-functions, 2937 Schenck, Hal. See Efremenko, Klim Schmitzer, Bernhard. See Chizat, Léna¨ıc INDEX TO VOLUME 87 (2018)

Schost, Eric.´ See Nogneng, Dorian Schratz, Katharina. See Baumstark, Simon Semplice, M. See Cravero, I. Shen, Jie. See Cai, Yongyong Shen, Jiguang. See Qiu, Weifeng Shen, Zuowei. See Han, Bin Shi, Ke. See Qiu, Weifeng Shurman, Jerry. See King, Oliver D. Siurys,ˇ J. See Drungilas, P. Sonar, Thomas. See Glaubitz, Jan Speidel, Ulrich. See Rebenich, Niko Stevenson, R. P. See Broersen, D. Stuart, Andrew M., and Aretha L. Teckentrup. Posterior consistency for Gaussian process approximations of Bayesian posterior distributions, 721 Su, Chunmei. See Bao, Weizhu Sutherland, Andrew V. See Daniels, Harris B. Szpruch,Lukasz, and X¯ıl´ıngZh¯ang. V -integrability, asymptotic stability and comparison property of explicit numerical schemes for non-linear SDEs, 755

Szymaszkiewicz, Lucjan. See Dabrowski,, Andrzej Tabata, Masahisa, and Shinya Uchiumi. An exactly computable Lagrange–Galerkin scheme for the Navier–Stokes equations and its error estimates, 39 Tangedal, Brett A. See Sands, Jonathan W. Teckentrup, Aretha L. See Stuart, Andrew M. Toint, Philippe L. See Morini, Benedetta Townsend, Alex, Marcus Webb, and Sheehan Olver. Fast polynomial transforms based on Toeplitz and Hankel matrices, 1913 Tran, Hoang. See Chkifa, Abdellah Trung, Ngo Viet. See Kemper, Gregor Tsai, Richard. See Kublik, Catherine Uchiumi, Shinya. See Tabata, Masahisa Van Anh, Nguyen Thi. See Kemper, Gregor Veronese, D. O. See Mart´ınez-Finkelshtein, A. Vialard, Fran¸cois-Xavier. See Chizat, Léna¨ıc Vinoles, Valentin. See Bécache, Eliane´ Visconti, G. See Cravero, I. Wang, Chunmei, and Junping Wang. A primal-dual weak Galerkin finite element method for second order elliptic equations in non-divergence form, 515 Wang, Junping. See Wang, Chunmei Wang, Li. See Coquel, Frédéric . See Liu, Jian-Guo Wang, Siyang, Anna Nissen, and Gunilla Kreiss. Convergence of finite difference methods for the wave equation in two space dimensions, 2737 Wang, Xiaojie. See Hutzenthaler, Martin Ward, J. D. See Hangelbroek, T. . See Lehoucq, R. B. Webb, Marcus. See Townsend, Alex Webster, Clayton G. See Chkifa, Abdellah Wen, Hairui. See Liu, Hailiang Wendland, Holger. See Ramming, Tobias Weyman, Jerzy. See Efremenko, Klim Widlund, Olof B. See Oh, Duk-Soon Wihler, Thomas P. See Houston, Paul Williams, D. M. An entropy stable, hybridizable discontinuous Galerkin method for the compressible Navier-Stokes equations, 95 Winther, Ragnar. See Lee, Jeonghun J. Wuthrich, Christian. Numerical modular symbols for elliptic curves, 2393 Xia, Binzhou. Cyclotomic difference sets in finite fields, 2461 Xu, Yuesheng. See Ma, Yunyun INDEX TO VOLUME 87 (2018)

Ye, Qiang. Accurate inverses for computing eigenvalues of extremely ill-conditioned matrices and diﬀerential operators, 237 Yserentant, Harry. See Kornhuber, Ralf Yuan, Yongjun. See Cai, Yongyong Yuen, David S. See King, Oliver D. Zampini, Stefano. See Oh, Duk-Soon Zhang, Hui. See Ju, Lili Zhang, Jiwei. See Zhang, Qian Zhang, Qian, Jiwei Zhang, Shidong Jiang, and Zhimin Zhang. Numerical solution to a linearized time fractional KdV equation on unbounded domains, 693 Zh¯ang,X¯ıl´ıng. See Szpruch,Lukasz Zhang, Zhimin. See Zhang, Qian Zhou, Yang, and Xiaojun Chen. Spherical t-designs for approximations on the sphere, 2831 Zhou, Zhennan. See Liu, Jian-Guo . See Lu, Jianfeng Zhuang, Xiaosheng. See Han, Bin Ziegler, G¨unter M. See Brinkmann, Philip Ziegler, Volker. See Krenn, Daniel Zimmer, C. See Altmann, R. VOLUME 87 2018

AMERICANMATHEMATICALSOCIETY

Simone Brugiapaglia, Fabio Nobile, Stefano Micheletti, and Simona Perotto, A theoretical study of COmpRessed SolvING for advection- diffusion-reaction problems ...... 1 Masahisa Tabata and Shinya Uchiumi, An exactly computable Lagrange–Galerkin scheme for the Navier–Stokes equations and its error estimates ...... 39 Weifeng Qiu, Jiguang Shen, and Ke Shi, An HDG method for linear elasticity with strong symmetric stresses ...... 69 D. M. Williams, An entropy stable, hybridizable discontinuous Galerkin method for the compressible Navier-Stokes equations ...... 95 Hailiang Liu and Hairui Wen, Error estimates for the AEDG method to one-dimensional linear convection-diffusion equations ...... 123 R. Altmann and C. Zimmer, Runge-Kutta methods for linear semi-explicit operator differential-algebraic equations ...... 149 Jan Glaubitz, Philipp Offner,¨ and Thomas Sonar, Application of modal filtering to a spectral difference method ...... 175 Steffen Börm, Adaptive compression of large vectors ...... 209 Qiang Ye, Accurate inverses for computing eigenvalues of extremely ill-conditioned matrices and differential operators ...... 237 A. Mart´ınez-Finkelshtein, A. Sri Ranga, and D. O. Veronese, Extreme zeros in a sequence of para-orthogonal polynomials and bounds for the support of the measure ...... 261 Pedro Freitas, Sharp bounds for the modulus and phase of Hankel functions with applications to Jaeger integrals ...... 289 Yunyun Ma and Yuesheng Xu, Computing highly oscillatory integrals . 309 Bin Han, Qingtang Jiang, Zuowei Shen, and Xiaosheng Zhuang, Symmetric canonical quincunx tight framelets with high vanishing moments and smoothness ...... 347 Nicolas Mascot, Certification of modular Galois representations ...... 381 Harris B. Daniels, Alvaro´ Lozano-Robledo, Filip Najman, and An- drew V. Sutherland, Torsion subgroups of rational elliptic curves over the compositum of all cubic fields ...... 425

Peter Bruin and Andrea Ferraguti, On L-functions of quadratic Q-curves 459 King Cheong Fung and Ben Kane, On sign changes of cusp forms and the halting of an algorithm to construct a supersingular elliptic curve with a given endomorphism ring ...... 501 Vol. 87, No. 310 March 2018

Chunmei Wang and Junping Wang, A primal-dual weak Galerkin finite element method for second order elliptic equations in non-divergence form ...... 515 Snorre H. Christiansen, On eigenmode approximation for Dirac equations: Differential forms and fractional Sobolev spaces ...... 547 J. C. Latchéand K. Saleh, A convergent staggered scheme for the variable density incompressible Navier-Stokes equations ...... 581 Erik Burman, Peter Hansbo, and Mats G. Larson, A cut finite element method with boundary value correction ...... 633 Duk-Soon Oh, Olof B. Widlund, Stefano Zampini, and Clark R. Dohrmann, BDDC Algorithms with deluxe scaling and adaptive selection of primal constraints for Raviart-Thomas vector fields ...... 659 Qian Zhang, Jiwei Zhang, Shidong Jiang, and Zhimin Zhang, Numerical solution to a linearized time fractional KdV equation on unbounded domains ...... 693 Andrew M. Stuart and Aretha L. Teckentrup, Posterior consistency for Gaussian process approximations of Bayesian posterior distributions . . 721 Lukasz Szpruch and X¯ıl´ıngZh¯ang, V -integrability, asymptotic stability and comparison property of explicit numerical schemes for non-linear SDEs ...... 755 Robert Plato, Peter Mathé,and Bernd Hofmann, Optimal rates for Lavrentiev regularization with adjoint source conditions ...... 785 Claude-Pierre Jeannerod and Siegfried M. Rump, On relative errors of floating-point operations: Optimal bounds and applications ...... 803 Daniel Krenn and Volker Ziegler, Non-minimality of the width-w non- adjacent form in conjunction with trace one τ-adic digit expansions and Koblitz curves in characteristic two ...... 821 Niko Rebenich, T. Aaron Gulliver, Stephen Neville, and Ulrich Speidel, An analog of the prime number theorem for finite fields via truncated polylogarithm expansions ...... 855 Oliver D. King, Cris Poor, Jerry Shurman, and David S. Yuen, Using Katsurada’s determination of the Eisenstein series to compute Siegel eigenforms ...... 879 Dorian Nogneng and Eric´ Schost, On the evaluation of some sparse polynomials ...... 893 Michael DiPasquale, Dimension of mixed splines on polytopal cells ...... 905 Ruyong Feng, On the computation of the Galois group of linear difference equations ...... 941 A. Detinko, D. L. Flannery, and A. Hulpke, Zariski density and computing in arithmetic groups ...... 967 William Kuszmaul, Fast algorithms for finding pattern avoiders and counting pattern occurrences in permutations ...... 987 Greg Hurst, Computations of the Mertens function and improved bounds on the Mertens conjecture ...... 1013 Vol. 87, No. 311 May 2018

Erik Burman and Peter Hansbo, Stabilized nonconforming finite element methods for data assimilation in incompressible flows ...... 1029 D. Broersen, W. Dahmen, and R. P. Stevenson, On the stability of DPG formulations of transport equations ...... 1051 FrédéricCoquel, Shi Jin, Jian-Guo Liu, and Li Wang, Entropic sub- cell shock capturing schemes via Jin-Xin relaxation and Glimm front sampling for scalar conservation laws ...... 1083 T. Gallouët,R. Herbin, J.-C. Latché,and D. Maltese, Convergence of the MAC scheme for the compressible stationary Navier-Stokes equations ...... 1127 Jian-Guo Liu, Li Wang, and Zhennan Zhou, Positivity-preserving and asymptotic preserving method for 2D Keller-Segal equations ...... 1165 Yongyong Cai and Yongjun Yuan, Uniform error estimates of the conservative finite difference method for the Zakharov system in the subsonic limit regime ...... 1191 Simon Baumstark, Erwan Faou, and Katharina Schratz, Uniformly accurate exponential-type integrators for Klein-Gordon equations with asymptotic convergence to the classical NLS splitting ...... 1227 Shmuel Friedland and Lek-Heng Lim, Nuclear norm of higher-order tensors ...... 1255 Wanyou Cheng and Yu-Hong Dai, Gradient-based method with active set strategy for `1 optimization ...... 1283 E. G. Birgin, N. Krejić,and J. M. Mart´ınez, On the employment of inexact restoration for the minimization of functions whose evaluation is subject to errors ...... 1307 Benedetta Morini, Margherita Porcelli, and Philippe L. Toint, Approximate norm descent methods for constrained nonlinear systems 1327 Martin Hutzenthaler, Arnulf Jentzen, and Xiaojie Wang, Exponential integrability properties of numerical approximation processes for nonlinear stochastic differential equations ...... 1353 Abdellah Chkifa, Nick Dexter, Hoang Tran, and Clayton G. Webster, Polynomial approximation via compressed sensing of high- dimensional functions on lower sets ...... 1415 Laura Faber and Habiba Kadiri, Corrigendum to New bounds for ψ(x) 1451 Enrique González-Jiménez and Alvaro´ Lozano-Robledo, On the torsion of rational elliptic curves over quartic fields ...... 1457 Hugo Labrande, Computing Jacobi’s theta in quasi-linear time ...... 1479

Andrzej Dabrowski, and Lucjan Szymaszkiewicz, Orders of Tate- Shafarevich groups for the Neumann-Setzer type elliptic curves ...... 1509 P. Drungilas, J. Jankauskas, and J. Siurys,ˇ On Littlewood and Newman polynomial multiples of Borwein polynomials ...... 1523 Vol. 87, No. 312 July 2018

A. Linke, C. Merdon, M. Neilan, and F. Neumann, Quasi-optimality of a pressure-robust nonconforming finite element method for the Stokes- problem ...... 1543 Hengguang Li, An anisotropic finite element method on polyhedral domains: Interpolation error analysis ...... 1567 Long Chen, Jun Hu, and Xuehai Huang, Fast auxiliary space preconditioners for linear elasticity in mixed form ...... 1601 Martin J. Gander and Soheil Hajian, Analysis of Schwarz methods for a hybridizable discontinuous Galerkin discretization: The many- subdomain case ...... 1635 Ruijian He, Xinlong Feng, and Zhangxin Chen, H1-Superconvergence of a difference finite element method based on the P1 − P1-conforming element on non-uniform meshes for the 3D Poisson equation ...... 1659 I. Cravero, G. Puppo, M. Semplice, and G. Visconti, CWENO: Uniformly accurate reconstructions for balance laws ...... 1689 Matt Elsey and Selim Esedo¯glu, Threshold dynamics for anisotropic surface energies ...... 1721 Tobias Ramming and Holger Wendland, A kernel-based discretisation method for first order partial differential equations ...... 1757 Lehel Banjai and Alexander Rieder, Convolution quadrature for the wave equation with a nonlinear impedance boundary condition ...... 1783 Gabriel Acosta, Juan Pablo Borthagaray, Oscar Bruno, and Mart´ın Maas, Regularity theory and high order numerical methods for the (1D)-fractional Laplacian ...... 1821 Lili Ju, Xiao Li, Zhonghua Qiao, and Hui Zhang, Energy stability and error estimates of exponential time differencing schemes for the epitaxial growth model without slope selection ...... 1859 Weizhang Huang and Lennard Kamenski, On the mesh nonsingularity of the moving mesh PDE method ...... 1887 Alex Townsend, Marcus Webb, and Sheehan Olver, Fast polynomial transforms based on Toeplitz and Hankel matrices ...... 1913 A. Melman, Eigenvalue bounds for matrix polynomials in generalized bases 1935 T. Hangelbroek, F. J. Narcowich, C. Rieger, and J. D. Ward, An inverse theorem for compact Lipschitz regions in Rd using localized kernel bases ...... 1949 Jan Büthe, An analytic method for bounding ψ(x) ...... 1991 Yoonjin Lee and Yoon Kyung Park, A continued fraction of order twelve as a modular function ...... 2011 Klim Efremenko, J. M. Landsberg, Hal Schenck, and Jerzy Weyman, The method of shifted partial derivatives cannot separate the permanent from the determinant ...... 2037 Zachary Charles, Generating random factored ideals in number fields . . . . 2047 Vol. 87, No. 313 September 2018

Yongyong Cai and Jie Shen, Error estimates for a fully discretized scheme to a Cahn-Hilliard phase-field model for two-phase incompressible flows 2057 Johnny Guzmánand Maxim Olshanskii, Inf-sup stability of geometrically unfitted Stokes finite elements ...... 2091 Sebastian Franz and Gunar Matthies, A unified framework for time- dependent singularly perturbed problems with discontinuous Galerkin methods in time ...... 2113 Weizhu Bao and Chunmei Su, Uniform error bounds of a finite difference method for the Klein-Gordon-Zakharov system in the subsonic limit regime ...... 2133 Philippe Angot and Rima Cheaytou, On the error estimates of the vector penalty-projection methods: Second-order scheme ...... 2159 Jianfeng Lu and Zhennan Zhou, Frozen Gaussian approximation with surface hopping for mixed quantum-classical dynamics: A mathematical justification of fewest switches surface hopping algorithms ...... 2189 R. B. Lehoucq, F. J. Narcowich, S. T. Rowe, and J. D. Ward, A meshless Galerkin method for non-local diffusion using localized kernel bases ...... 2233 Kassem Mustapha, FEM for time-fractional diffusion equations, novel optimal error analyses ...... 2259 V. J. Ervin, N. Heuer, and J. P. Roop, Regularity of the solution to 1- D fractional order diffusion equations ...... 2273 Yiannis Hadjimichael and David I. Ketcheson, Strong-stability- preserving additive linear multistep methods ...... 2295 L. Lopez and S. Maset, Time-transformations for the event location in discontinuous ODEs ...... 2321 Bjoern Bringmann, Daniel Cremers, Felix Krahmer, and Michael Moeller, The homotopy method revisited: Computing solution paths of `1-regularized problems ...... 2343 Catherine Kublik and Richard Tsai, An extrapolative approach to integration over hypersurfaces in the level set framework ...... 2365 Christian Wuthrich, Numerical modular symbols for elliptic curves ...... 2393 José Ignacio Burgos Gil, Ricardo Menares, and Juan Rivera- Letelier, On the essential minimum of Faltings’ height ...... 2425 Binzhou Xia, Cyclotomic difference sets in finite fields ...... 2461 Lo¨ıcGreniéand Giuseppe Molteni, Explicit bounds for generators of the class group ...... 2483 Gregor Kemper, Ngo Viet Trung, and Nguyen Thi Van Anh, Toward a theory of monomial preorders ...... 2513 Maria Bras-Amorósand Julio Fernández-González, Computation of numerical semigroups by means of seeds ...... 2539 Janne I. Kokkala and Patric R. J. Osterg˚ard,¨ The chromatic number of the square of the 8-cube ...... 2551 Vol. 87, No. 314 November 2018

Léna¨ıcChizat, Gabriel Peyré,Bernhard Schmitzer, and Fran¸cois- Xavier Vialard, Scaling algorithms for unbalanced optimal transport problems ...... 2563 Christian Kreuzer and Emmanuil H. Georgoulis, Convergence of adaptive discontinuous Galerkin methods ...... 2611 Paul Houston and Thomas P. Wihler, An hp-adaptive Newton- discontinuous-Galerkin finite element approach for semilinear elliptic boundary value problems ...... 2641 Andrea Cangiani, Emmanuil H. Georgoulis, and Younis A. Sabawi, Adaptive discontinuous Galerkin methods for elliptic interface problems 2675 Jeonghun J. Lee and Ragnar Winther, Local coderivatives and approximation of Hodge Laplace problems ...... 2709 Siyang Wang, Anna Nissen, and Gunilla Kreiss, Convergence of finite difference methods for the wave equation in two space dimensions . . . . 2737 Ralf Kornhuber, Daniel Peterseim, and Harry Yserentant, An analysis of a class of variational multiscale methods based on subspace decomposition ...... 2765 Eliane´ Bécache, Patrick Joly, and Valentin Vinoles, On the analysis of perfectly matched layers for a class of dispersive media and application to negative index metamaterials ...... 2775 Dario A. Bini, Stefano Massei, and Beatrice Meini, Semi-infinite quasi- Toeplitz matrices with applications to QBD stochastic processes ...... 2811 Yang Zhou and Xiaojun Chen, Spherical t-designs for approximations on the sphere ...... 2831 Zhijian He, Quasi-Monte Carlo for discontinuous integrands with singularities along the boundary of the unit cube ...... 2857 Jared Duker Lichtman and Carl Pomerance, Improved error bounds for the Fermat primality test on random inputs ...... 2871 Andrew R. Booker, Finite connected components of the aliquot graph . . 2891 St˚alAanderaa, Lars Kristiansen, and Hans Kristian Ruud, Search for good examples of Hall’s conjecture ...... 2903 Markus Hittmeir, A babystep-giantstep method for faster deterministic integer factorization ...... 2915 Jonathan W. Sands and Brett A. Tangedal, Computing annihilators of class groups from derivatives of L-functions ...... 2937 Philip Brinkmann and Günter M. Ziegler, Small f-vectors of 3-spheres and of 4-polytopes ...... 2955 Frédéric Chyzak, Thomas Dreyfus, Philippe Dumas, and Marc Mezzarobba, Computing solutions of linear Mahler equations ...... 2977 Javier Cilleruelo, Florian Luca, and Lewis Baxter, Every positive integer is a sum of three palindromes ...... 3023 Editorial Information Information on the backlog for this journal can be found on the AMS website starting from http://www.ams.org/mcom. In an effort to make articles available as quickly as possible, articles are electronically published on the AMS website individually after proof is returned from authors and before appearing in an issue. A Consent to Publish is required before we can begin processing your paper. After a paper is accepted for publication, the Providence office will send a Consent to Publish and Copyright Agreement to all authors of the paper. By submitting a paper to this journal, authors certify that the results have not been submitted to nor are they under considera- tion for publication by another journal, conference proceedings, or similar publication.

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Inquiries. Any inquiries concerning a paper that has been accepted for publication that cannot be answered via the manuscript tracking system mentioned above should be sent to [email protected] or directly to the Electronic Prepress Department, American Mathematical Society, 201 Charles Street, Providence, RI 02904-2213 USA. Editorial Committee SUSANNE C. BRENNER, Chair, Center for Computation & Technology and Depart- ment of Mathematics, Louisiana State University, Baton Rouge, LA 70803 USA; E-mail: [email protected] IGOR E. SHPARLINSKI, Department of Pure Mathematics, University of New South Wales, Sydney, NSW 2052, Australia; E-mail: [email protected] CHI-WANG SHU, Applied Mathematics Division, Brown University, P.O. Box F, 182 George St., Providence, RI 02912-0001 USA; E-mail: [email protected] DANIEL B. SZYLD, Department of Mathematics 038-16, Temple University, 638 Wachman, 1805 N. Broad St. Philadelphia, PA 19122-6094 USA; E-mail: [email protected]

Board of Associate Editors DANIELE BOFFI, Department of Mathematics, University di Pavia, Via Ferrata 1, 27100 Pavia PV, Italy; E-mail: [email protected] MARTIN BURGER, Institut für Numerische und Angewandte Mathematik, West- faelisch Wilhelms-Universität Münster, Einsteinstr. 62, D-48149 Münster, Germany; E-mail: [email protected] ALBERT COHEN, Laboratoire Jacques-Louis Lions, Université Pierre et Marie Curie, 4, Place Jussieu, 75005 Paris, France; E-mail: [email protected] RONALD F. A. COOLS, Department of Computer Science, Katholieke Universiteit Leuven, Celestijnenlaan 200A, B-3001 Heverlee, Belgium; E-mail: ronald.cools@cs. kuleuven.ac.be BRUNO DESPRES, University of Paris VI, Laboratory Jacques-Louis Lions, 175 rue du Chevaleret, 75013 Paris, France; E-mail: [email protected] QIANG DU, Columbia University, 500 W 120th Street, APAM, 200 Mudd, MC 4701, New York, NY 10027, USA; E-mail: [email protected] BETTINA EICK, Institut Computational Mathematics, University of Braunschweig, 38106 Braunschweig, Germany; E-mail: [email protected] HOWARD C. ELMAN, Department of Computer Science, University of Maryland, College Park, MD 20742 USA; E-mail: [email protected] IVAN G. GRAHAM, Department of Mathematical Sciences, University of Bath, Bath BA2 7AY, United Kingdom; E-mail: [email protected] RALF HIPTMAIR, Department of Mathematics, Seminar of Applied Mathematics, ETH Zurich, CH-8092 Zurich, Switzerland. E-mail: [email protected] MARK van HOEIJ, Department of Mathematics, Florida State University, 1017 Aca- demic Way, Tallahassee, FL 32306 USA; E-mail: [email protected] FRANCES KUO, University of New South Wales, School of Mathematics, Sydney NSW 2052, Australia; E-mail: [email protected] SVEN LEYFFER, Mathematics and Computer Science Division, Argonne National Laboratory, Argonne, IL 60439, USA; E-mail: [email protected] CHRISTIAN LUBICH, Mathematisches Institut, Universität Tübingen, Auf der Mor- genstelle 10, 72076 Tübingen, Germany; E-mail: [email protected] GUNTER MALLE, Fachbereich Mathematik, Universität Kaiserslautern, Postfach 3049, 67653 Kaiserslautern, Germany; E-mail: [email protected] ANDREI MARTÍNEZ-FINKELSHTEIN, Department of Mathematics, Baylor Univer- sity, Waco, TX 76798 USA; and Department of Mathematics, University of Almeria, 04120 Almeria, Spain; E-mail: a [email protected] JAMES MCKEE, Department of Mathematics, Royal Holloway University of London, Egham Hill, Egham TW20 0EX, United Kingdom; E-mail: [email protected] MICHAEL J. MOSSINGHOFF, Department of Mathematics, Davidson College, Box 6996, Davidson, NC 28035-6996 USA; E-mail: [email protected] MICHAEL J. NEILAN, Department of Mathematics, University of Pittsburgh, Pitts- burgh, PA 15260 USA; E-mail: [email protected] FABIO NOBILE, Mathematics Institute of Computational Science and Engineering, Ecole´ Polytechnique Fédérale de Lausanne, CH 1015 Lausanne, Switzerland; E-mail: [email protected] ADAM M. OBERMAN, Department of Mathematics and Statistics, McGill University, 805 Sherbrooke St W, Montreal QC H3A 0B9, Canada; E-mail: [email protected] FRANK-OLAF SCHREYER, Faculty of Mathematics and Computer Science, Saarland University, Campus E2 4, 66123 Saarbrücken, Germany; E-mail: [email protected] CHRISTOPH SCHWAB, Seminar for Applied Mathematics, ETH Zürich, Raemistrasse 101, HG G57.1, CH-8092 Zürich, Switzerland; E-mail: [email protected] ZUOWEI SHEN, Department of Mathematics, National University of Singapore, Block S17 10, Lower Kent Ridge Road, 119076 Singapore; E-mail: [email protected] ANDREW V. SUTHERLAND, Department of Mathematics, Massachusetts Institute of Technology, Cambridge, MA 02139 USA; E-mail: [email protected] HANS VOLKMER, Department of Mathematical Sciences, University of Wisconsin- Milwaukee, P.O. Box 413, Milwaukee, WI 53201-0413 USA; E-mail: [email protected] BARBARA WOHLMUTH, Fakultät für Mathematik, Technische Universität München, Boltzmannstr. 3, 85748 Garching, Germany; E-mail: [email protected] (Continued from back cover) Philip Brinkmann and Günter M. Ziegler, Small f-vectors of 3-spheres and of 4-polytopes ...... 2955 Frédéric Chyzak, Thomas Dreyfus, Philippe Dumas, and Marc Mezzarobba, Computing solutions of linear Mahler equations ...... 2977 Javier Cilleruelo, Florian Luca, and Lewis Baxter, Every positive integer is a sum of three palindromes ...... 3023 ahmtc fComputation of Mathematics MATHEMATICS OF COMPUTATION CONTENTS Vol. 87, No. 314 November 2018

Yang Zhou and Xiaojun Chen, Spherical t-designs for approximations on the sphere ...... 2831 Zhijian He, Quasi-Monte Carlo for discontinuous integrands with singularities along the boundary of the unit cube ...... 2857 Jared Duker Lichtman and Carl Pomerance, Improved error bounds for the Fermat primality test on random inputs ...... 2871 Andrew R. Booker, Finite connected components of the aliquot graph . . 2891 St˚alAanderaa, Lars Kristiansen, and Hans Kristian Ruud, Search for good examples of Hall’s conjecture ...... 2903 Markus Hittmeir, A babystep-giantstep method for faster deterministic integer factorization ...... 2915 Jonathan W. Sands and Brett A. Tangedal, Computing annihilators of class groups from derivatives of L-functions ...... 2937 (Continued on inside back cover)

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