Ameya Pitale: Siegel Modular Forms

Cover: 9783030156749 | Siegel Modular Forms | Ameya Pitale | Taschenbuch | ix | Englisch

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Beschreibung

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.

Zusammenfassung

Explores the connections between the classical and representation theoretic approaches in the study of Siegel modular forms

Illustrates how basic concepts can be applied to solve contemporary problems in the study of modular forms

Based on lecture notes delivered during a workshop at the Indian Institutes of Science Education and Research, Pune, India from 2017

Inhaltsverzeichnis

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(¿p).- 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.

Details

Erscheinungsjahr:	2019
Fachbereich:	Wahrscheinlichkeitstheorie
Genre:	Mathematik , Medizin , Naturwissenschaften , Technik
Rubrik:	Naturwissenschaften & Technik
Medium:	Taschenbuch
Reihe:	Lecture Notes in Mathematics
Inhalt:	ix 138 S. 112 s/w Illustr. 138 p. 112 illus.
ISBN-13:	9783030156749
ISBN-10:	3030156745
Sprache:	Englisch
Herstellernummer:	978-3-030-15674-9
Einband:	Kartoniert / Broschiert
Autor:	Pitale, Ameya
Hersteller:	Springer Palgrave Macmillan Springer International Publishing AG Lecture Notes in Mathematics
Verantwortliche Person für die EU:	Springer Verlag GmbH, Tiergartenstr. 17, D-69121 Heidelberg, juergen.hartmann@springer.com
Maße:	235 x 155 x 9 mm
Von/Mit:	Ameya Pitale
Erscheinungsdatum:	08.05.2019
Gewicht:	0,236 kg