03075nam 22006255 450 991076029550332120251009095736.09783031431920303143192810.1007/978-3-031-43192-0(PPN)273590766(MiAaPQ)EBC30870257(Au-PeEL)EBL30870257(DE-He213)978-3-031-43192-0(CKB)28781944700041(EXLCZ)992878194470004120231106d2023 u| 0engurcnu||||||||txtrdacontentcrdamediacrrdacarrierRepresentations of SU(2,1) in Fourier Term Modules /by Roelof W. Bruggeman, Roberto J. Miatello1st ed. 2023.Cham :Springer Nature Switzerland :Imprint: Springer,2023.1 online resource (217 pages)Lecture Notes in Mathematics,1617-9692 ;2340Print version: Bruggeman, Roelof W. Representations of SU(2,1) in Fourier Term Modules Cham : Springer,c2023 9783031431913 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.Lecture Notes in Mathematics,1617-9692 ;2340Number theoryFourier analysisTopological groupsLie groupsNumber TheoryFourier AnalysisTopological Groups and Lie GroupsNumber theory.Fourier analysis.Topological groups.Lie groups.Number Theory.Fourier Analysis.Topological Groups and Lie Groups.515.2433515.2433Bruggeman Roelof W56659Miatello Roberto J1437763MiAaPQMiAaPQMiAaPQBOOK9910760295503321Representations of SU(2,1) in Fourier Term Modules3598646UNINA