Representations of SU(2,1) in Fourier term modules / Roelof W. Bruggeman, Roberto J. Miatello.

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Representations of SU(2,1) in Fourier term modules / Roelof W. Bruggeman, Roberto J. Miatello.

9783031431920 (electronic bk.)
3031431928 (electronic bk.)
9783031431913
303143191X

Cham : Springer, [2023]

©2023

English

1 online resource (xi, 210 pages) : illustrations (chiefly color).

10.1007/978-3-031-43192-0 doi

QA403.5

515/.2433

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 Poincar ̌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 Poincar ̌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.

Includes bibliographical references and index.

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Online resource; title from PDF title page (SpringerLink, viewed November 13, 2023).

Lecture notes in mathematics (Springer-Verlag) ; 2340.

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