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商品詳細
Representations of SU(2,1) in Fourier Term Modules. 1st ed. 2023.
・ISBN 978-3-031-43191-3 paper EUR 54.99
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| 著者・編者 | Bruggeman, Roelof W. / Miatello, Roberto J., |
|---|---|
| シリーズ | Lecture Notes in Mathematics |
| 出版社 | (Springer International Publishing AG, SZ) |
| 出版年月 | 2023 |
| ページ数 | 210 pp. |
| 言語 | ENG |
| ニュース番号 | ＜M25-16635＞ |
解説
This book studies the modules arising in Fourier expansions of automorphic forms, namely Fourier term modules on SU(2,1), the smallest rank one Lie group with a non-abelian unipotent subgroup. It considers the "abelian" Fourier term modules connected to characters of the maximal unipotent subgroups of SU(2,1), and also the "non-abelian" modules, described via theta functions. A complete description of the submodule structure of all Fourier term modules is given, with a discussion of the consequences for Fourier expansions of automorphic forms, automorphic forms with exponential growth included.
These results can be applied to prove a completeness result for Poincare series in spaces of square integrable automorphic forms.
Aimed at researchers and graduate students interested in automorphic forms, harmonic analysis on Lie groups, and number-theoretic topics related to Poincare series, the book will also serve as a basic reference on spectral expansion with Fourier-Jacobi coefficients. Only a background in Lie groups and their representations is assumed.
These results can be applied to prove a completeness result for Poincare series in spaces of square integrable automorphic forms.
Aimed at researchers and graduate students interested in automorphic forms, harmonic analysis on Lie groups, and number-theoretic topics related to Poincare series, the book will also serve as a basic reference on spectral expansion with Fourier-Jacobi coefficients. Only a background in Lie groups and their representations is assumed.