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＜電子ブック＞
Representations of SU(2,1) in Fourier Term Modules / by Roelof W. Bruggeman, Roberto J. Miatello
(Lecture Notes in Mathematics. ISSN:16179692 ; 2340)

版	1st ed. 2023.
出版者	(Cham : Springer Nature Switzerland : Imprint: Springer)
出版年	2023
本文言語	英語
大きさ	XI, 210 p. 66 illus., 51 illus. in color : online resource
著者標目	*Bruggeman, Roelof W author Miatello, Roberto J author SpringerLink (Online service)
件　名	LCSH:Number theory LCSH:Fourier analysis LCSH:Topological groups LCSH:Lie groups FREE:Number Theory FREE:Fourier Analysis FREE:Topological Groups and Lie Groups
一般注記	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 asa basic reference on spectral expansion with Fourier-Jacobi coefficients. Only a background in Lie groups and their representations is assumed HTTP:URL=https://doi.org/10.1007/978-3-031-43192-0

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