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Record Nr. |
UNINA9910760295503321 |
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Autore |
Bruggeman Roelof W |
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Titolo |
Representations of SU(2,1) in Fourier Term Modules / / by Roelof W. Bruggeman, Roberto J. Miatello |
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Pubbl/distr/stampa |
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Cham : , : Springer Nature Switzerland : , : Imprint : Springer, , 2023 |
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ISBN |
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Edizione |
[1st ed. 2023.] |
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Descrizione fisica |
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1 online resource (217 pages) |
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Collana |
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Lecture Notes in Mathematics, , 1617-9692 ; ; 2340 |
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Altri autori (Persone) |
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Disciplina |
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Soggetti |
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Number theory |
Fourier analysis |
Topological groups |
Lie groups |
Number Theory |
Fourier Analysis |
Topological Groups and Lie Groups |
Teoria de nombres |
Anàlisi de Fourier |
Llibres electrònics |
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Lingua di pubblicazione |
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Formato |
Materiale a stampa |
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Livello bibliografico |
Monografia |
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Sommario/riassunto |
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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, |
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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. |
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