LEADER 03213nam 22006615 450 001 9910760295503321 005 20240626145755.0 010 $a3-031-43192-8 024 7 $a10.1007/978-3-031-43192-0 035 $a(MiAaPQ)EBC30870257 035 $a(Au-PeEL)EBL30870257 035 $a(DE-He213)978-3-031-43192-0 035 $a(CKB)28781944700041 035 $a(EXLCZ)9928781944700041 100 $a20231106d2023 u| 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aRepresentations of SU(2,1) in Fourier Term Modules /$fby Roelof W. Bruggeman, Roberto J. Miatello 205 $a1st ed. 2023. 210 1$aCham :$cSpringer Nature Switzerland :$cImprint: Springer,$d2023. 215 $a1 online resource (217 pages) 225 1 $aLecture Notes in Mathematics,$x1617-9692 ;$v2340 311 08$aPrint version: Bruggeman, Roelof W. Representations of SU(2,1) in Fourier Term Modules Cham : Springer,c2023 9783031431913 330 $aThis book studies the modules arising in Fourier expansions of automorphic forms, namely Fourier term modules on SU(2,1), the smallest rank one Lie group with a non-abelian unipotent subgroup. It considers the ?abelian? Fourier term modules connected to characters of the maximal unipotent subgroups of SU(2,1), and also the ?non-abelian? modules, described via theta functions. A complete description of the submodule structure of all Fourier term modules is given, with a discussion of the consequences for Fourier expansions of automorphic forms, automorphic forms with exponential growth included. These results can be applied to prove a completeness result for Poincaré series in spaces of square integrable automorphic forms. Aimed at researchers and graduate students interested in automorphic forms, harmonic analysis on Lie groups, and number-theoretic topics related to Poincaré series, the book will also serve as a basic reference on spectral expansion with Fourier-Jacobi coefficients. Only a background in Lie groups and their representations is assumed. 410 0$aLecture Notes in Mathematics,$x1617-9692 ;$v2340 606 $aNumber theory 606 $aFourier analysis 606 $aTopological groups 606 $aLie groups 606 $aNumber Theory 606 $aFourier Analysis 606 $aTopological Groups and Lie Groups 606 $aTeoria de nombres$2thub 606 $aAnàlisi de Fourier$2thub 608 $aLlibres electrònics$2thub 615 0$aNumber theory. 615 0$aFourier analysis. 615 0$aTopological groups. 615 0$aLie groups. 615 14$aNumber Theory. 615 24$aFourier Analysis. 615 24$aTopological Groups and Lie Groups. 615 7$aTeoria de nombres 615 7$aAnàlisi de Fourier 676 $a515.2433 676 $a515.2433 700 $aBruggeman$b Roelof W$056659 701 $aMiatello$b Roberto J$01437763 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910760295503321 996 $aRepresentations of SU(2,1) in Fourier Term Modules$93598646 997 $aUNINA