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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Fuchsian groups of convergence type and nontangential growth of automorphic forms


Authors: T. A. Metzger and K. V. Rajeswara Rao
Journal: Proc. Amer. Math. Soc. 48 (1975), 135-139
MathSciNet review: 0357778
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Abstract: For a Fuchsian group, it is shown that the nontangential growth of automorphic forms characterizes whether or not the group is of convergence type. As a corollary of the main result, it is shown that for a Fuchsian group of second kind, not necessarily finitely generated, every integrable automorphic form of dimension $ - 2$ is zero, thus extending a known result.


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DOI: https://doi.org/10.1090/S0002-9939-1975-0357778-0
Article copyright: © Copyright 1975 American Mathematical Society