| Description |
1 online resource (xi, 210 pages) : illustrations (chiefly color) |
| Series |
Lecture notes in mathematics, 1617-9692 ; volume 2340 |
|
Lecture notes in mathematics (Springer-Verlag) ; 2340. 1617-9692
|
| Summary |
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 |
| Bibliography |
Includes bibliographical references and index |
| Notes |
Online resource; title from PDF title page (SpringerLink, viewed November 13, 2023) |
| Subject |
Fourier analysis.
|
|
Fourier analysis
|
| Form |
Electronic book
|
| Author |
Miatello, Roberto J., author.
|
| ISBN |
9783031431920 |
|
3031431928 |
|
