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Title
Siegel modular forms : a classical and representation-theoretic approach / Ameya Pitale.
ISBN
9783030156756 (electronic book)
3030156753 (electronic book)
9783030156749
Published
Cham, Switzerland : Springer, 2019.
Language
English
Description
1 online resource (ix, 138 pages) : illustrations.
Item Number
10.1007/978-3-030-15675-6 doi
10.1007/978-3-030-15
Call Number
QA243
Dewey Decimal Classification
512.7/3
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.
Bibliography, etc. Note
Includes bibliographical references and index.
Access Note
Access limited to authorized users.
Source of Description
Online resource; title from PDF title page (SpringerLink, viewed May 17, 2019).
Series
Lecture notes in mathematics (Springer-Verlag) ; 2240.
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.
