Siegel Modular Forms
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Siegel Modular Forms
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Author : Ameya Pitale
language : en
Publisher: Springer
Release Date : 2019-05-07
Siegel Modular Forms written by Ameya Pitale and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-05-07 with Mathematics categories.
This monograph introduces two approaches to studying Siegel modular forms: the classical approach as holomorphic functions on the Siegel upper half space, and the approach via representation theory on the symplectic group. By illustrating the interconnections shared by the two, this book fills an important gap in the existing literature on modular forms. It begins by establishing the basics of the classical theory of Siegel modular forms, and then details more advanced topics. After this, much of the basic local representation theory is presented. Exercises are featured heavily throughout the volume, the solutions of which are helpfully provided in an appendix. Other topics considered include Hecke theory, Fourier coefficients, cuspidal automorphic representations, Bessel models, and integral representation. Graduate students and young researchers will find this volume particularly useful. It will also appeal to researchers in the area as a reference volume. Some knowledge of GL(2) theory is recommended, but there are a number of appendices included if the reader is not already familiar.
Introduction To Siegel Modular Forms And Dirichlet Series
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Author : Anatoli Andrianov
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-03-17
Introduction To Siegel Modular Forms And Dirichlet Series written by Anatoli Andrianov and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-03-17 with Mathematics categories.
Several years ago I was invited to an American university to give one-term graduate course on Siegel modular forms, Hecke operators, and related zeta functions. The idea to present in a concise but basically complete and self-contained form an int- duction to an important and developing area based partly on my own work attracted me. I accepted the invitation and started to prepare the course. Unfortunately, the visit was not realized. But the idea of such a course continued to be alive till after a number of years this book was ?nally completed. I hope that this short book will serve to attract young researchers to this beautiful ?eld, and that it will simplify and make more pleasant the initial steps. No special knowledge is presupposed for reading this book beyond standard courses in algebra and calculus (one and several variables), although some skill in working with mathematical texts would be helpful. The reader will judge whether the result was worth the effort. Dedications. The ideas of Goro Shimura exerted a deep in?uence on the number theory of the second half of the twentieth century in general and on the author’s formation in particular. When Andre ` Weil was signing a copy of his “Basic Number Theory” to my son, he wrote in Russian, ”To Fedor Anatolievich hoping that he will become a number theoretist”. Fedor has chosen computer science. Now I pass on the idea to Fedor’s daughter, Alexandra Fedorovna.
Introductory Lectures On Siegel Modular Forms
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Author : Helmut Klingen
language : en
Publisher: Cambridge University Press
Release Date : 2008-05-15
Introductory Lectures On Siegel Modular Forms written by Helmut Klingen and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-05-15 with Mathematics categories.
This volume aims to present a straightforward and easily accessible survey of the analytic theory of quadratic forms. Written at an elementary level, the book provides a sound basis from which the reader can study advanced works and undertake original research. Roughly half a century ago C.L. Siegel discovered a new type of automorphic forms in several variables in connection with his famous work on the analytic theory of quadratic forms. Since then Siegel modular forms have been studied extensively because of their significance in both automorphic functions in several complex variables and number theory. The comprehensive theory of automorphic forms to subgroups of algebraic groups and the recent arithmetical theory of modular forms illustrate these two aspects in an illuminating manner. The text is based on the author's lectures given over a number of years and is intended for a one semester graduate course, although it can serve equally well for self study . The only prerequisites are a knowledge of algebra, number theory and complex analysis.
Siegel S Modular Forms And Dirichlet Series
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Author : Hans Maaß
language : en
Publisher:
Release Date : 1969
Siegel S Modular Forms And Dirichlet Series written by Hans Maaß and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1969 with categories.
Siegel S Modular Forms And Dirichlet Series
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Author : Hans Maass
language : en
Publisher:
Release Date : 2014-09-01
Siegel S Modular Forms And Dirichlet Series written by Hans Maass and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-09-01 with categories.
Siegel S Modular Forms And Dirichlet Series
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Author : Hans Maaß
language : en
Publisher: Springer
Release Date : 2006-11-15
Siegel S Modular Forms And Dirichlet Series written by Hans Maaß and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-15 with Mathematics categories.
These notes present the content of a course I delivered at the University of Maryland, College Park, between September 1969 and April 1970. The choice of the subject was mainly determined by my intention to show how Atle Selberg makes fascinating use of differential operators in order to prove certain functional equations. Of course one has to be somewhat familiar with his theory of weakly symmetric Riemannian spaces, but - as Selberg himself pointed out to me the main idea can be found already in Riemann's work. Since Selberg never published his idea, it might be of some value for the mathematical community to make available to a wider public the methods which were originally conceived by Selberg a long time ago.
Lectures On Siegel Modular Forms And Representation By Quadratic Forms
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Author : Yoshiyuki Kitaoka
language : en
Publisher:
Release Date : 1986
Lectures On Siegel Modular Forms And Representation By Quadratic Forms written by Yoshiyuki Kitaoka and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1986 with Forms (Mathematics). categories.
Non Archimedean L Functions And Arithmetical Siegel Modular Forms
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Author : Michel Courtieu
language : en
Publisher: Springer
Release Date : 2003-12-15
Non Archimedean L Functions And Arithmetical Siegel Modular Forms written by Michel Courtieu and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-12-15 with Mathematics categories.
This book, now in its 2nd edition, is devoted to the arithmetical theory of Siegel modular forms and their L-functions. The central object are L-functions of classical Siegel modular forms whose special values are studied using the Rankin-Selberg method and the action of certain differential operators on modular forms which have nice arithmetical properties. A new method of p-adic interpolation of these critical values is presented. An important class of p-adic L-functions treated in the present book are p-adic L-functions of Siegel modular forms having logarithmic growth. The given construction of these p-adic L-functions uses precise algebraic properties of the arithmetical Shimura differential operator. The book will be very useful for postgraduate students and for non-experts looking for a quick approach to a rapidly developing domain of algebraic number theory. This new edition is substantially revised to account for the new explanations that have emerged in the past 10 years of the main formulas for special L-values in terms of arithmetical theory of nearly holomorphic modular forms.
Compactification Of Siegel Moduli Schemes
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Author : Ching-Li Chai
language : en
Publisher: Cambridge University Press
Release Date : 1985-12-12
Compactification Of Siegel Moduli Schemes written by Ching-Li Chai and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1985-12-12 with Mathematics categories.
The main result of this monograph is to prove the existence of the toroidal compactification over Z(1/2).
Non Archimedean L Functions And Arithmetical Siegel Modular Forms
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Author : Michel Courtieu
language : en
Publisher:
Release Date : 2014-09-01
Non Archimedean L Functions And Arithmetical Siegel Modular Forms written by Michel Courtieu and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-09-01 with categories.