TY - BOOK ID - 127352158 TI - Representations of SU(2,1) in Fourier Term Modules AU - Bruggeman, Roelof W. AU - Miatello, Roberto J. PY - 2023 SN - 3031431928 PB - Cham : Springer Nature Switzerland : Imprint: Springer, DB - UniCat KW - Number theory. KW - Fourier analysis. KW - Topological groups. KW - Lie groups. KW - Number Theory. KW - Fourier Analysis. KW - Topological Groups and Lie Groups. KW - Teoria de nombres KW - Anàlisi de Fourier UR - https://www.unicat.be/uniCat?func=search&query=sysid:127352158 AB - 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. ER -