Introduction To Siegel Modular Forms And Dirichlet Series
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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.
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.
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:
Release Date : 1971
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 1971 with Dirichlet series categories.
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 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.
Hecke S Theory Of Modular Forms And Dirichlet Series
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Author : Bruce C. Berndt
language : en
Publisher: World Scientific
Release Date : 2008
Hecke S Theory Of Modular Forms And Dirichlet Series written by Bruce C. Berndt and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Mathematics categories.
Cyber security, encompassing both information and network security, is of utmost importance in today's information age. Cyber Security Standards, Practices and Industrial Applications: Systems and Methodologies details the latest and most important advances in security standards. First, it introduces the differences between information security (covers the understanding of security requirements, classification of threats, attacks and information protection systems and methodologies) and network security (includes both security protocols as well as systems which create a security perimeter around networks for intrusion detection and avoidance). In addition, the book serves as an essential reference to students, researchers, practitioners, and consultants in the area of social media, cyber security and information, and communication technologies (ICT).
Modular Forms And Dirichlet Series
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Author : Andrew Ogg
language : en
Publisher:
Release Date : 1969
Modular Forms And Dirichlet Series written by Andrew Ogg and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1969 with Dirichlet series categories.
Modular Forms A Classical Approach
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Author : Henri Cohen
language : en
Publisher: American Mathematical Soc.
Release Date : 2017-08-02
Modular Forms A Classical Approach written by Henri Cohen and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-08-02 with Forms (Mathematics). categories.
The theory of modular forms is a fundamental tool used in many areas of mathematics and physics. It is also a very concrete and “fun” subject in itself and abounds with an amazing number of surprising identities. This comprehensive textbook, which includes numerous exercises, aims to give a complete picture of the classical aspects of the subject, with an emphasis on explicit formulas. After a number of motivating examples such as elliptic functions and theta functions, the modular group, its subgroups, and general aspects of holomorphic and nonholomorphic modular forms are explained, with an emphasis on explicit examples. The heart of the book is the classical theory developed by Hecke and continued up to the Atkin–Lehner–Li theory of newforms and including the theory of Eisenstein series, Rankin–Selberg theory, and a more general theory of theta series including the Weil representation. The final chapter explores in some detail more general types of modular forms such as half-integral weight, Hilbert, Jacobi, Maass, and Siegel modular forms. Some “gems” of the book are an immediately implementable trace formula for Hecke operators, generalizations of Haberland's formulas for the computation of Petersson inner products, W. Li's little-known theorem on the diagonalization of the full space of modular forms, and explicit algorithms due to the second author for computing Maass forms. This book is essentially self-contained, the necessary tools such as gamma and Bessel functions, Bernoulli numbers, and so on being given in a separate chapter.