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Siegel Modular Forms = A Classical and Representation-Theoretic Approach /

Record Type:	Language materials, printed : Monograph/item
Title/Author:	Siegel Modular Forms/ by Ameya Pitale.
Reminder of title:	A Classical and Representation-Theoretic Approach /
Author:	Pitale, Ameya.
Description:	IX, 138 p. 112 illus.online resource. :
Contained By:	Springer Nature eBook
Subject:	Number theory. -
Online resource:	https://doi.org/10.1007/978-3-030-15675-6
ISBN:	9783030156756

Siegel Modular Forms = A Classical and Representation-Theoretic Approach /
Pitale, Ameya.

Siegel Modular FormsA Classical and Representation-Theoretic Approach /[electronic resource] :by Ameya Pitale. - 1st ed. 2019. - IX, 138 p. 112 illus.online resource. - Lecture Notes in Mathematics,22400075-8434 ;. - Lecture Notes in Mathematics,2144.

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.

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.

ISBN: 9783030156756

Standard No.: 10.1007/978-3-030-15675-6doiSubjects--Topical Terms:

527883
Number theory.

LC Class. No.: QA241-247.5

Dewey Class. No.: 512.7

Siegel Modular Forms = A Classical and Representation-Theoretic Approach /
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