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Transactions of the American Mathematical Society
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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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1973-0337791-2
PII: S 0002-9947(1973)0337791-2
Keywords: Automorphic function, automorphic form, entire, discontinuous group
Article copyright: © Copyright 1973 American Mathematical Society