Lecture Notes in Mathematics

Siegel Modular Forms

A Classical and Representation-Theoretic Approach

Authors: Pitale, Ameya

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  • 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
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  • ISBN 978-3-030-15675-6
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About this book

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.

Table of contents (10 chapters)

Table of contents (10 chapters)

Buy this book

eBook 32,12 €
price for Spain (gross)
  • ISBN 978-3-030-15675-6
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover 41,59 €
price for Spain (gross)
  • ISBN 978-3-030-15674-9
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
  • The final prices may differ from the prices shown due to specifics of VAT rules
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Bibliographic Information

Bibliographic Information
Book Title
Siegel Modular Forms
Book Subtitle
A Classical and Representation-Theoretic Approach
Authors
Series Title
Lecture Notes in Mathematics
Series Volume
2240
Copyright
2019
Publisher
Springer International Publishing
Copyright Holder
Springer Nature Switzerland AG
eBook ISBN
978-3-030-15675-6
DOI
10.1007/978-3-030-15675-6
Softcover ISBN
978-3-030-15674-9
Series ISSN
0075-8434
Edition Number
1
Number of Pages
IX, 138
Number of Illustrations
112 b/w illustrations
Topics