springer.com/booksellers Springer News 11/12/2008 Mathematics 37 V. Adamyan, Y. Berezansky, I. Gohberg, V. Adamyan, Y. Berezansky, I. Gohberg, V. Adamyan (Ed.) M. L. Gorbachuk, V. Gorbachuk, A. N. Kochubei, M. L. Gorbachuk, V. Gorbachuk, A. N. Kochubei, H. Langer, G. Popov (Eds.) H. Langer,G. Popov (Eds.) Modern Analysis and Modern Analysis and Modern Analysis and Applications Applications Applications The Mark Krein Centenary Conference The Mark Krein Centenary Conference – The Mark Krein Centenary Conference – Volume 1 Volume 2 These two volumes contain peer-reviewed research and survey papers based on invited talks at the This is the first of two volumes containing peer- This is the second of two volumes containing International Conference on Modern Analysis reviewed research and survey papers based on peer-reviewed research and survey papers based and Applications. The conference, which was invited talks at the International Conference on on invited talks at the International Confer- dedicated to the 100th anniversary of the birth of Modern Analysis and Applications. The confer- ence on Modern Analysis and Applications. The Mark Krein, one of the greatest mathematicians ence, which was dedicated to the 100th anni- conference, which was dedicated to the 100th of the 20th century, was held in Odessa, Ukraine, versary of the birth of Mark Krein, one of the anniversary of the birth of Mark Krein, one of the on April 9-14, 2007. The papers describe the greatest mathematicians of the 20th century, was greatest mathematicians of the 20th century, was contemporary development of subjects influenced held in Odessa, Ukraine, on April 9-14, 2007. The held in Odessa, Ukraine, on April 9-14, 2007. The by Krein, such as the theory of operators in Hilbert papers describe the contemporary development of papers describe the contemporary development of and Krein spaces, differential operators, applica- subjects influenced by Krein, such as the theory of subjects influenced by Krein, such as the theory of tions of functional analysis in function theory, operators in Hilbert and Krein spaces, differential operators in Hilbert and Krein spaces, differential theory of networks and systems, mathematical operators, applications of functional analysis in operators, applications of functional analysis in physics and mechanics. function theory, theory of networks and systems, function theory, theory of networks and systems, mathematical physics and mechanics. mathematical physics and mechanics. Features 7 Wide panorama of the development of func- Features Features tional analysis, operator theory, and their applica- 7 Wide panorama of the development of func- 7 Wide panorama of the development of func- tions 7 Many contributions by active members of tional analysis, operator theory, and their applica- tional analysis, operator theory, and their applica- scientific schools founded by Mark Krein tions 7 Many contributions by active members of tions 7 Many contributions by active members of scientific schools founded by Mark Krein scientific schools founded by Mark Krein Fields of interest Analysis; Operator Theory; Functional Analysis Fields of interest Fields of interest Analysis; Operator Theory; Functional Analysis Analysis; Operator Theory; Functional Analysis Target groups Researchers in operator theory, functional analysis, Target groups Target groups and integral equations Researchers in operator theory, functional analysis, Researchers in operator theory, functional analysis, and integral equations and integral equations Type of publication Commemorative publication Type of publication Type of publication Commemorative publication Commemorative publication Mathematics Mathematics Mathematics Due April 2009 Due April 2009 Due April 2009 2009. Approx. 500 p. (Operator Theory) Hardcover 2009. Approx. 500 p. (Operator Theory) Hardcover 2009. Approx. 1000 p. (2-volume-set) (Operator Theory) 7 € 169,00 | £133.50 7 € 169,00 | £133.50 7 € 299,00 | £236.50 9<HTOHRE=djjbie>ISBN 978-3-7643-9918-4 9<HTOHRE=djjcah>ISBN 978-3-7643-9920-7 9<HTOHRE=djjcef>ISBN 978-3-7643-9924-5 38 Mathematics Springer News 11/12/2008 springer.com/booksellers A. Andrianov, Russian Academy of the Sciences, S. Barwick, University of Adelaide, SA, Australia; D. J. Bernstein, J. Buchmann, E. Dahmen (Eds.) St. Petersburg, Russia G. Ebert, University of Delaware, Newark, DE, USA Post Quantum Cryptography Introduction to Siegel Unitals in Projective Planes Modular Forms and Dirichlet Series Quantum computers will break today’s most This book is a monograph on unitals embedded in popular public-key cryptographic systems, finite projective planes. Unitals are key structures including RSA, DSA, and ECDSA. This book This is intended for a graduate course on Siegel in projective planes, and have connections with introduces the reader to the next generation of modular forms, Hecke operators, and related zeta other structures in algebra. They play a signifi- cryptographic algorithms, the systems that resist functions. The author’s aim is to present a concise cant role in the classification of finite planes and quantum-computer attacks: in particular, post- and self-contained introduction to an important provide a link between groups and geometries. quantum public-key encryption systems and post- and developing area of number theory that will There is a considerable number of research articles quantum public-key signature systems. serve to attract young researchers to this beautiful about unitals, and there also exist many open Leading experts have joined forces for the first field. problems. This book is a thorough survey of the time to explain the state of the art in quantum Topics include: -analytical properties of radial research literature on embedded unitals which computing, hash-based cryptography, code-based Dirichlet series attached to modular forms of collects this material in book form for the first cryptography, lattice-based cryptography, and genuses 1 and 2; - the abstract theory of Hecke– time. The book is aimed at graduate students and multivariate cryptography. Mathematical founda- Shimura rings for symplectic and related groups; researchers who want to learn about this topic tions and implementation issues are included. -action of Hecke operators on Siegel modular without reading all the original articles. This book is an essential resource for students and forms; -applications of Hecke operators to a study The primary proof techniques used involve linear researchers who want to contribute to the field of of multiplicative properties of Fourier coeffi- algebraic arguments, finite field arithmetic, some post-quantum cryptography. cients of modular forms; -Hecke zeta functions of elementary number theory, and combinatorial modular forms in one variable and to spinor (or enumeration. Some computer results not previ- Features Andrianov) zeta functions of Siegel modular forms ously found in the literature also are mentioned in 7 Contributors to the book take on the big chal- of genus two; -the proof of analytical continuation the text. lenge in cryptography, namely: what to do when and functional equation (under certain assump- someone will break the crypto-systems of today tions) for Euler products associated with modular Features forms of genus two. 7 No other book on unitals, book will fill that Fields of interest void 7 Text is clear and easy to follow 7 Book is Number Theory; Data Encryption; Mathematics of Features well-structured and comprehensive with excellent Computing 7 Will become a standard reference on the subject diagrams 7 Intended for graduate students and keeps Target groups prerequisites to a minimum 7 Gives provocative Contents Cryptologists in mathematics, computer science, examples in the simplest and most accessible terms Preface.- Preliminaries.- Hermitian curves and engineering, and industry 7 Author is an expert who has originated many unitals.- Translation planes.- Unitals embedded important ideas in the subject in desarguesian planes.- Unitals embedded in Type of publication non-desarguesian planes.- Combinatorial ques- Contributed volume Contents tions and associated configurations.- Character- Preface.- Introduction: The Two Features ization results.- Open problems.- Nomenclature of Arithmetical Zeta Functions.- Modular of unitals.- Group theoretic characterizations of Forms.- Dirichlet Series of Modular Forms.- unitals.- References.- Notation index.- Index. Hecke-Shimura Rings of Double Cosets.- Hecke Operators.- Euler Factorization of Radial Series.- Fields of interest Conclusion: Other Groups, Other Horizons.- Geometry; Combinatorics; Algebra Notes.- Short Bibliography.- Target groups Fields of interest Graduate students and researchers Number Theory; Algebra Type of publication Target groups Monograph Graduate students, researchers Type of publication Graduate/Advanced undergraduate textbook Mathematics Mathematics Mathematics Due December 2008 Due December 2008 Due December 2008 2009. XII, 196 p. 29 illus. (Springer Monographs in 2009. Approx. 210 p. (Universitext) Softcover Mathematics) Hardcover 2009. XII, 245 p. Hardcover 7 € 42,95 | £32.50 7 € 54,95 | £43.99 7 approx. € 59,95 | £47.99 9<HTLDTH=hihfch>ISBN 978-0-387-78752-7 9<HTLDTH=hgdgee>ISBN 978-0-387-76364-4 9<HTOFPA=iihaba>ISBN 978-3-540-88701-0 springer.com/booksellers Springer News 11/12/2008 Mathematics 39 L. A. Bokut, E. Zelmanov, I. Shestakov, V. Latyshev W. J. Cook, L. Lovász, J. Vygen (Eds.) A. Deitmar, University of Tübingen, Germany; (Eds.) S. Echterhoff, University of