Introductory Lectures On Siegel Modular Forms

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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.

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 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 areaas 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.

The 1 2 3 Of Modular Forms

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Author : Jan Hendrik Bruinier
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-02-10

The 1 2 3 Of Modular Forms written by Jan Hendrik Bruinier 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 2008-02-10 with Mathematics categories.

This book grew out of three series of lectures given at the summer school on "Modular Forms and their Applications" at the Sophus Lie Conference Center in Nordfjordeid in June 2004. The first series treats the classical one-variable theory of elliptic modular forms. The second series presents the theory of Hilbert modular forms in two variables and Hilbert modular surfaces. The third series gives an introduction to Siegel modular forms and discusses a conjecture by Harder. It also contains Harder's original manuscript with the conjecture. Each part treats a number of beautiful applications.

Modular Forms A Classical And Computational Introduction 2nd Edition

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Author : Lloyd James Peter Kilford
language : en
Publisher: World Scientific Publishing Company
Release Date : 2015-03-12

Modular Forms A Classical And Computational Introduction 2nd Edition written by Lloyd James Peter Kilford and has been published by World Scientific Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-03-12 with Mathematics categories.

Modular Forms is a graduate student-level introduction to the classical theory of modular forms and computations involving modular forms, including modular functions and the theory of Hecke operators. It also includes applications of modular forms to various subjects, such as the theory of quadratic forms, the proof of Fermat's Last Theorem and the approximation of π. The text gives a balanced overview of both the theoretical and computational sides of its subject, allowing a variety of courses to be taught from it.This second edition has been revised and updated. New material on the future of modular forms as well as a chapter about longer-form projects for students has also been added.

Automorphic Forms

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Author : Bernhard Heim
language : en
Publisher: Springer
Release Date : 2014-11-19

Automorphic Forms written by Bernhard Heim and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-11-19 with Mathematics categories.

This edited volume presents a collection of carefully refereed articles covering the latest advances in Automorphic Forms and Number Theory, that were primarily developed from presentations given at the 2012 “International Conference on Automorphic Forms and Number Theory,” held in Muscat, Sultanate of Oman. The present volume includes original research as well as some surveys and outlines of research altogether providing a contemporary snapshot on the latest activities in the field and covering the topics of: Borcherds products Congruences and Codes Jacobi forms Siegel and Hermitian modular forms Special values of L-series Recently, the Sultanate of Oman became a member of the International Mathematical Society. In view of this development, the conference provided the platform for scientific exchange and collaboration between scientists of different countries from all over the world. In particular, an opportunity was established for a close exchange between scientists and students of Germany, Oman, and Japan. The conference was hosted by the Sultan Qaboos University and the German University of Technology in Oman.

L Functions And Automorphic Forms

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Author : Jan Hendrik Bruinier
language : en
Publisher: Springer
Release Date : 2018-02-22

L Functions And Automorphic Forms written by Jan Hendrik Bruinier and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-02-22 with Mathematics categories.

This book presents a collection of carefully refereed research articles and lecture notes stemming from the Conference "Automorphic Forms and L-Functions", held at the University of Heidelberg in 2016. The theory of automorphic forms and their associated L-functions is one of the central research areas in modern number theory, linking number theory, arithmetic geometry, representation theory, and complex analysis in many profound ways. The 19 papers cover a wide range of topics within the scope of the conference, including automorphic L-functions and their special values, p-adic modular forms, Eisenstein series, Borcherds products, automorphic periods, and many more.

Automorphic Forms And Zeta Functions Proceedings Of The Conference In Memory Of Tsuneo Arakawa

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Author : Masanobu Kaneko
language : en
Publisher: World Scientific
Release Date : 2006-01-03

Automorphic Forms And Zeta Functions Proceedings Of The Conference In Memory Of Tsuneo Arakawa written by Masanobu Kaneko and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-01-03 with Mathematics categories.

This volume contains a valuable collection of articles presented at a conference on Automorphic Forms and Zeta Functions in memory of Tsuneo Arakawa, an eminent researcher in modular forms in several variables and zeta functions. The book begins with a review of his works, followed by 16 articles by experts in the fields including H Aoki, R Berndt, K Hashimoto, S Hayashida, Y Hironaka, H Katsurada, W Kohnen, A Krieg, A Murase, H Narita, T Oda, B Roberts, R Schmidt, R Schulze-Pillot, N Skoruppa, T Sugano, and D Zagier. A variety of topics in the theory of modular forms and zeta functions are covered: Theta series and the basis problems, Jacobi forms, automorphic forms on Sp(1, q), double zeta functions, special values of zeta and L-functions, many of which are closely related to Arakawa's works.This collection of papers illustrates Arakawa's contributions and the current trends in modular forms in several variables and related zeta functions.

Modular Forms

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Author : Henri Cohen
language : en
Publisher: American Mathematical Soc.
Release Date : 2017-08-02

Modular Forms 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 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.

Automorphic Forms And L Functions Ii

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Author : David Ginzburg
language : en
Publisher: American Mathematical Soc.
Release Date : 2009

Automorphic Forms And L Functions Ii written by David Ginzburg 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 2009 with Mathematics categories.

Includes articles that represent global aspects of automorphic forms. This book covers topics such as: the trace formula; functoriality; representations of reductive groups over local fields; the relative trace formula and periods of automorphic forms; Rankin - Selberg convolutions and L-functions; and, p-adic L-functions.