Siegel Modular Forms : A Classical and Representation-Theoretic Approach / by Ameya Pitale.

Format:

Book

Author/Creator:

Pitale, Ameya, 1977- author.

Contributor:

SpringerLink (Online service)

Series:

Mathematics and Statistics (Springer-11649)

Lecture Notes in Mathematics, 0075-8434 ; 2240.

Lecture Notes in Mathematics, 0075-8434 ; 2240

Language:

English

Subjects (All):

Number theory.

Group theory.

Number Theory.

Group Theory and Generalizations.

Local Subjects:

Number Theory.

Group Theory and Generalizations.

Physical Description:

1 online resource (IX, 138 pages) : 112 illustrations.

Edition:

First edition 2019.

Contained In:

Springer eBooks

Place of Publication:

Cham : Springer International Publishing : Imprint: Springer, 2019.

System Details:

text file PDF

Summary:

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.

Contents:

Introduction

Lecture 1:Introduction to Siegel modular forms

Lecture 2: Examples

Lecture 3: Hecke Theory and L-functions

Lecture 4: Non-vanishing of primitive Fourier coefficients and applications

Lecture 5: Applications of properties of L-functions

Lecture 6: Cuspidal automorphic representations corresponding to Siegel modular forms

Lecture 7: Local representation theory of GSp4(ℚp)

Lecture 8: Bessel models and applications

Lecture 9: Analytic and arithmetic properties of GSp4 x GL2 L-functions

Lecture 10: Integral representation of the standard L-function.

Other Format:

Printed edition:

ISBN:

978-3-030-15675-6

9783030156756

Access Restriction:

Restricted for use by site license.