03213nam 22006615 450 991076029550332120240626145755.03-031-43192-810.1007/978-3-031-43192-0(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 as a 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 GroupsTeoria de nombresthubAnàlisi de FourierthubLlibres electrònicsthubNumber theory.Fourier analysis.Topological groups.Lie groups.Number Theory.Fourier Analysis.Topological Groups and Lie Groups.Teoria de nombresAnàlisi de Fourier515.2433515.2433Bruggeman Roelof W56659Miatello Roberto J1437763MiAaPQMiAaPQMiAaPQBOOK9910760295503321Representations of SU(2,1) in Fourier Term Modules3598646UNINA