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View This Volume's Front and Back Matter Number Theory and Its Applications in China AMERICAn MATHEMATICAL SOCIETY u0 LU mE 77 http://dx.doi.org/10.1090/conm/077 Titles in This Series Volume 1 Markov random fields and their 18 Fixed points and nonexpansive applications, Ross Kindermann and mappings. Robert C. Sine, Editor J. Laurie Snell 19 Proceedings of the Northwestern 2 Proceedings of the conference homotopy theory conference, on integration, topology, and Haynes R. Miller and Stewart B. geometry in linear spaces, Priddy, Editors William H. Graves. Editor 20 Low dimensional topology, 3 The closed graph and P-closed Samuel J. Lomonaco. Jr., Editor graph properties in general 21 Topological methods in nonlinear topology, T. R. Hamlett and functional analysis, S. P. Singh, L. L. Herrington S. Thomeier, and B. Watson. Editors 4 Problems of elastic stability and 22 Factorizations of b" ± 1, b = vibrations, Vadim Komkov, Editor 2. 3. 5. 6. 7, 10, 5 Rational constructions of 11. 12 up to high powers, modules for simple Lie algebras, John Brillhart. D. H. Lehmer. George B. Seligman J. L. Selfridge, Bryant Tuckerman, and 6 Umbral calculus and Hopf algebras, S. S. Wagstaff, Jr. Robert Morris, Editor 23 Chapter 9 of Ramanujan's second 7 Complex contour integral notebook-Infinite series identities, representation of cardinal spline transformations, and evaluations, functions, Walter Schempp Bruce C. Berndt and Padmini T. Joshi 8 Ordered fields and real algebraic 24 Central extensions, Galois groups, geometry, D. W. Dubois and and ideal class groups of numiJer T. Recio. Editors fields, A. Frohlich 9 Papers in algebra, analysis and 25 Value distribution theory and its statistics. R. Lidl, Editor applications, Chung-Chun Yang, 10 Operator algebras and K-theory, Editor Ronald G. Douglas and Claude 26 Conference in modern analysis Schochet. Editors and probability, Richard Beals, 11 Plane ellipticity and related Anatole Beck. Alexandra Bellow. and problems, Robert P. Gilbert, Editor Arshag Hajian. Editors 12 Symposium on algebraic topology in 27 Microlocal analysis, M. Salah honor of Jos~ Adem, Samuel Gitler, Baouendi. Richard Beals, and Editor Linda Preiss Rothschild, Editors 13 Algebraists' homage: Papers in 28 Fluids and plasmas: geometry and ring theory and related topics, dynamics, Jerrold E. Marsden, Editor S. A. Amitsur. D. J. Saltman, and 29 Automated theorem proving, G. B. Seligman. Editors W. W. Bledsoe and Donald Loveland. 14 Lectures on Nielsen fixed point Editors theory, Boju Jiang 30 Mathematical applications of 15 Advanced analytic number theory. category theory, J. W. Gray, Editor Part 1: Ramification theoretic 31 Axiomatic set theory, James E. methods, Carlos J. Moreno Baumgartner, Donald A. Martin, and 16 Complex representations of Saharon Shelah. Editors GL(2. K) for finite fields K. 32 Proceedings of the conference llya Piatetski-Shapiro on Banach algebras and several 17 Nonlinear partial differential complex variables, F. Greenleaf and equations, Joel A. Smoller. Editor D. Gulick, Editors Titles in This Series Volume 33 Contributions to group theory, 50 Random matrices and their Kenneth I. Appel, John G. Ratcliffe. applications, Joel E. Cohen, Harry and Paul E. Schupp, Editors Kesten, and Charles M. Newman, 34 Combinatorics and algebra, Editors Curtis Greene, Editor 51 Nonlinear problems in geometry, 35 Four-manifold theory, Cameron Dennis M. DeTurck, Editor Gordon and Robion Kirby, Editors 52 Geometry of normed linear 36 Group actions on manifolds, spaces, R. G. Bartle, N. T. Peck, Reinhard Schultz, Editor A. L. Peressini, and J. J. Uhl, Editors 37 Conference on algebraic topology 53 The Selberg trace formula and in honor of Peter Hilton. related topics, Dennis A. Hejhal, Renzo Piccinini and Denis Sjerve, Peter Sarnak, and Audrey Anne Terras, Editors Editors 38 Topics in complex analysis, 54 Differential analysis and Dorothy Browne Shaffer. Editor infinite dimensional spaces, Kondagunta Sundaresan and 39 Errett Bishop: Reflections Srinivasa Swaminathan, Editors on him and his research, 55 Applications of algebraic K-theory Murray Rosenblatt, Editor to algebraic geometry and 40 Integral bases for affine Lie algebras number theory, Spencer J. Bloch, and their universal enveloping R. Keith Dennis, Eric M. Friedlander, algebras, David Mitzman and Michael R. Stein, Editors 41 Particle systems, random 56 Multiparameter bifurcation theory, media and large deviations, Martin Golubitsky and John Richard Durrett, Editor Guckenheimer, Editors 42 Classical real analysis, Daniel 57 Combinatorics and ordered sets, Waterman, Editor Ivan Rival, Editor 43 Group actions on rings, Susan 58.1 The Lefschetz centennial Montgomery, Editor conference. Part 1: Proceedings 44 Combinatorial methods in on algebraic geometry, topology and algebraic geometry, D. Sundararaman, Editor John R. Harper and Richard 58.11 The Lefschetz centennial Mandelbaum, Editors conference. Part II: Proceedings on 45 Finite groups-coming of age, algebraic topology, S. Gitler, Editor John McKay, Editor 58.111 The Lefschetz centennial 46 Structure of the standard modules conference. Part Ill: Proceedings for the affine Lie algebra A11), on differential equations, James Lepowsky and Mirko Prime A. Verjovsky, Editor 47 Linear algebra and its role in 59 Function estimates, J. S. Marron, systems theory, Richard A. Brualdi, Editor David H. Carlson, Biswa Nath Datta, 60 Nonstrictly hyperbolic conservation Charles R. Johnson, and Robert J. laws, Barbara Lee Keyfitz and Plemmons, Editors Herbert C. Kranzer, Editors 48 Analytic functions of one complex 61 Residues and traces of differential variable, Chung-chun Yang and forms via Hochschild homology, Chi-tai Chuang, Editors Joseph Lipman 49 Complex differential geometry and 62 Operator algebras and mathematical nonlinear differential equations, physics, Palle E. T. Jorgensen and Yum- Tong Siu, Editor Paul S. Muhly, Editors Titles in This Series Volume 63 Integral geometry, Robert L. Bryant. 71 Mathematics and general relativity, Victor Guillemin. Sigurdur Helgason. James A. Isenberg. Editor and R. 0. Wells, Jr.. Editors 72 Fixed point theory and its 64 The legacy of Sonya Kovalevskaya, applications. R. F. Brown. Editor Linda Keen. Editor 73 Geometry of random motion, 65 Logic and combinatorics, Rick Durrett and Mark A. Pinsky, Stephen G. Simpson, Editor Editors 66 Free group rings, Narian Gupta 74 Geometry of group representations, 67 Current trends in arithmetical William M. Goldman and Andy R. algebraic geometry, Kenneth A. Magid, Editors Ribet, Editor 75 The finite calculus associated 68 Differential geometry: The with Bessel functions, Frank M. interface between pure and applied Cholewinski mathematics, Mladen luksic, 76 The structure of finite algebras, Clyde Martin, and William Shadwick, David C. Hobby and Ralph Mckenzie Editors 77 Number theory and its applications 69 Methods and applications of in China, Wang Yuan, Yang mathematical logic, Walter A. Chung-chun. and Pan Cheng-biao. Carnielli and luiz Paulo de Alcantara. Editors Editors 70 Index theory of elliptic operators, foliations, and operator algebras, Jerome Kaminker. Kenneth C. Millett, and Claude Schochet. Editors Volume77 Number Theory and Its Applications in China Wang Yuan1 Yang Chung-chun1 and Pan Chengbiao1 Editors AMERICAn MATHEMATICAL SOCIETY Providence • RhOde Island EDITORIAL BOARD Irwin Kra, managing editor M. Salah Baouendi William H. Jaco Daniel M. Burns Gerald J. Janusz David Eisenbud Jan Mycielski Jonathan Goodman 1980 Mathematics Subject Classification (1985 Revision). Primary 11. Library of Congress Cataloging-In-Publication Data Number theory and its applications in China/Wang Yuan. Yang Chung-chun, and Pan Cheng-biao, editors. p. em. - (Contemporary mathematics. ISSN 0271-4132; v. 77) Bibliography: p. ISBN 0-8218-5084-9 (alk. paper) 1. Numbers. Theory of-Research-China. I. Wang, Yuan. fl. 1963-. II. Yang. Chung-Chun, 1942- Ill. Pan. Cheng-biao. IV. Series: Contemporary mathematics (American Mathematical Society); v. 77. QA241.N8673 1988 88-19373 512 1.7-dc 19 CIP Copying and reprinting. Individual readers of this publication, and nonprofit libraries acting 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 pub- lication (including abstracts) is permitted only under license from the American Mathematical Society. Requests for such permission should be addressed to the Executive Director. American Mathematical Society, P.O. Box 6248, Providence. Rhode Island 02940. The appearance of the code on the first page of an article in this book indicates the copyright owner's consent for copying beyond that permitted by Sections 107 or 108 of the U.S. Copyright Law, provided that the fee of $1.00 plus $.25 per page for each copy be paid directly to the Copyright Clearance Center. Inc., 21 Congress Street, Salem. Massachusetts 01970. This consent does not extend to other kinds of copying, such as copying for general distribution. for advertising or promotional purposes. for creating new collective works, or for resale. Copyright @1988 by the American Mathematical Society. All rights reserved. The American Mathematical Society retains all rights except those granted to the United States Government. Printed in the United States of America. This volume was printed directly from author-prepared copy. The
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