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Lecture Notes in Mathematics
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Lecture Notes in Mathematics
Bruggeman, Roelof W.; Miatello, Roberto J.
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.
Details
Published by: Springer
Publication Date: 2023-11-07
Format: Paperback
ISBN-13: 9783031431913
DOI: 10.1007/978-3-031-43192-0
Dimensions: 235cm x155cm
Pages: 210