Representations of SU(2,1) in Fourier Term Modules / / by Roelof W. Bruggeman, Roberto J. Miatello

• Autore: Bruggeman Roelof W
• Pubblicazione: Cham : , : Springer Nature Switzerland : , : Imprint : Springer, , 2023
• Edizione: 1st ed. 2023.
• Descrizione fisica: 1 online resource (217 pages)
• Disciplina: 515.2433
• Soggetto topico: Number theory; Fourier analysis; Topological groups; Lie groups; Number Theory; Fourier Analysis; Topological Groups and Lie Groups
• Altri autori: MiatelloRoberto J
• Sommario/riassunto: 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.
• Titolo autorizzato: Representations of SU(2,1) in Fourier Term Modules
• ISBN: 9783031431920; 3031431928
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Lingua di pubblicazione: Inglese
• Record Nr.: 9910760295503321
• Lo trovi qui: Univ. Federico II
• Serie: Lecture Notes in Mathematics, . 1617-9692 ; ; 2340