Fuchsian groups of convergence type and nontangential growth of automorphic forms

Metzger, T. A.; Rajeswara Rao, K. V.

doi:10.1090/S0002-9939-1975-0357778-0

Fuchsian groups of convergence type and nontangential growth of automorphic forms
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Proc. Amer. Math. Soc. 48 (1975), 135-139 Request permission

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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Additional Information

Journal: Proc. Amer. Math. Soc. 48 (1975), 135-139
DOI: https://doi.org/10.1090/S0002-9939-1975-0357778-0
MathSciNet review: 0357778