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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Functions automorphic on large domains

Author: David A. James
Journal: Trans. Amer. Math. Soc. 181 (1973), 385-400
MSC: Primary 10D15
MathSciNet review: 0337791
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Abstract: For a discontinuous group $ \Gamma \subset {\text{SL}}(2,R)$, Poincaré produced a corresponding nonconstant automorphic form, meromorphic on the open upper half plane $ {\Pi ^ + }$. When the domain of meromorphicity grows larger than $ {\Pi ^ + }$, the type of group which can support an automorphic form is restricted, and the corresponding forms are generally quite simple. A complete analysis of this phenomenon is presented, with examples which show results are best possible.

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Keywords: Automorphic function, automorphic form, entire, discontinuous group
Article copyright: © Copyright 1973 American Mathematical Society

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