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ON THE FOURIER COEFFICIENTS OF SIEGEL MODULAR FORMS

Part of: Discontinuous groups and automorphic forms

Published online by Cambridge University Press:  21 October 2016

SIEGFRIED BÖCHERER  and
WINFRIED KOHNEN
SIEGFRIED BÖCHERER
Affiliation:
Institut für Mathematik, Universität Mannheim, D-68131 Mannheim, Germany email boecherer@math.uni-mannheim.de
WINFRIED KOHNEN
Affiliation:
Universität Heidelberg, Mathematisches Institut, INF 205, D-69120 Heidelberg, Germany email winfried@mathi.uni-heidelberg.de
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Abstract

One can characterize Siegel cusp forms among Siegel modular forms by growth properties of their Fourier coefficients. We give a new proof, which works also for more general types of modular forms. Our main tool is to study the behavior of a modular form for $Z=X+iY$ when $Y\longrightarrow 0$.

MSC classification

Primary: 11F30: Fourier coefficients of automorphic forms 11F46: Siegel modular groups; Siegel and Hilbert-Siegel modular and automorphic forms
Type
Article
Information
Nagoya Mathematical Journal , Volume 234 , June 2019 , pp. 1 - 16
Copyright
© 2016 Foundation Nagoya Mathematical Journal  

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