Ameya Pitale's Books

Siegel Modular Forms

A Classical and Representation-Theoretic Approach

By: Ameya Pitale

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Siegel Modular Forms

A Classical and Representation-Theoretic Approach

By: Ameya Pitale

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.

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Page Count

142

Publisher

Springer

Published Date

ISBN 10

3030156753

ISBN 13

9783030156756

Transfer of Siegel Cusp Forms of Degree 2

By: Ameya Pitale,Abhishek Saha,Ralf Schmidt

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Transfer of Siegel Cusp Forms of Degree 2

By: Ameya Pitale,Abhishek Saha,Ralf Schmidt

Let be the automorphic representation of generated by a full level cuspidal Siegel eigenform that is not a Saito-Kurokawa lift, and be an arbitrary cuspidal, automorphic representation of . Using Furusawa's integral representation for combined with a pullback formula involving the unitary group , the authors prove that the -functions are "nice". The converse theorem of Cogdell and Piatetski-Shapiro then implies that such representations have a functorial lifting to a cuspidal representation of . Combined with the exterior-square lifting of Kim, this also leads to a functorial lifting of to a cuspidal representation of . As an application, the authors obtain analytic properties of various -functions related to full level Siegel cusp forms. They also obtain special value results for and

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Page Count

120

Publisher

American Mathematical Soc.

Published Date

ISBN 10

0821898566

ISBN 13

9780821898567

Siegel Modular Forms

A Classical and Representation-Theoretic Approach

By: Ameya Pitale

Write a review Read reviews Take a Quiz Solve Book Puzzle

Siegel Modular Forms

A Classical and Representation-Theoretic Approach

By: Ameya Pitale

Average ratings

N/A

Write a review

Solve jigsaw puzzle

Age

Page Count

142

Publisher

Springer

Published Date

ISBN 10

3030156753

ISBN 13

9783030156756

Book's by Ameya Pitale

Siegel Modular Forms

Siegel Modular Forms

Transfer of Siegel Cusp Forms of Degree 2

Transfer of Siegel Cusp Forms of Degree 2

Siegel Modular Forms

Siegel Modular Forms

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