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

Edition	1st ed. 2023.
Publisher	(Cham : Springer Nature Switzerland : Imprint: Springer)
Year	2023
Language	English
Size	XI, 210 p. 66 illus., 51 illus. in color : online resource
Authors	*Bruggeman, Roelof W author Miatello, Roberto J author SpringerLink (Online service)
Subjects	LCSH:Number theory LCSH:Fourier analysis LCSH:Topological groups LCSH:Lie groups FREE:Number Theory FREE:Fourier Analysis FREE:Topological Groups and Lie Groups
Notes	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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