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Spectral decomposition of compactly supported Poincaré series and existence of cusp forms

Part of: Discontinuous groups and automorphic forms

Published online by Cambridge University Press:  22 January 2010

Goran Muić
Goran Muić*
Affiliation:
Department of Mathematics, University of Zagreb, Bijenička 30, 10000 Zagreb, Croatia (email: gmuic@math.hr)
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Abstract

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In this paper we address the issue of existence of cusp forms by using an extension and refinement of a classic method involving (adelic) compactly supported Poincaré series. As a consequence of our adelic approach, we also deal with cusp forms for congruence subgroups.

Keywords

cuspidal automorphic formsPoincaré series

MSC classification

Secondary: 11F70: Representation-theoretic methods; automorphic representations over local and global fields
Type
Research Article
Information
Compositio Mathematica , Volume 146 , Issue 1 , January 2010 , pp. 1 - 20
Copyright
Copyright © Foundation Compositio Mathematica 2010

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