| 書目名稱 | Representations of SU(2,1) in Fourier Term Modules | | 編輯 | Roelof W. Bruggeman,Roberto J. Miatello | | 視頻video | http://file.papertrans.cn/828/827499/827499.mp4 | | 概述 | Describes the structure of Fourier term modules.Gives complete Fourier-Jacobi expansions for SU(2,1).Provides computations in the Mathematica notebook | | 叢書名稱 | Lecture Notes in Mathematics | | 圖書封面 |  | | 描述 | 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 Poincaré 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 Poincaré 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.. | | 出版日期 | Book 2023 | | 關(guān)鍵詞 | Fourier Tem Modules; SU(2,1); Automorphic Form; Fourier-Jacobi Series; Unitary Group SU(2,1),; Non-Abelia | | 版次 | 1 | | doi | https://doi.org/10.1007/978-3-031-43192-0 | | isbn_softcover | 978-3-031-43191-3 | | isbn_ebook | 978-3-031-43192-0Series ISSN 0075-8434 Series E-ISSN 1617-9692 | | issn_series | 0075-8434 | | copyright | The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerl |
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