Functions automorphic on large domains
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- by David A. James PDF
- Trans. Amer. Math. Soc. 181 (1973), 385-400 Request permission
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.References
- Charles W. Curtis and Irving Reiner, Representation theory of finite groups and associative algebras, Pure and Applied Mathematics, Vol. XI, Interscience Publishers (a division of John Wiley & Sons, Inc.), New York-London, 1962. MR 0144979 L. Ford, Automorphic functions, Chelsea, New York, 1951. D. James, Automorphic forms on domains larger than the upper half plane, and factors of automorphy, Ph. D. Thesis, University of Wisconsin, Madison, Wis., 1970.
- Marvin Isadore Knopp, Polynomial automorphic forms and nondiscontinuous groups, Trans. Amer. Math. Soc. 123 (1966), 506–520. MR 200447, DOI 10.1090/S0002-9947-1966-0200447-7
- Joseph Lehner, A short course in automorphic functions, Holt, Rinehart and Winston, New York-Toronto, Ont.-London, 1966. MR 0201637
- H. Poincare, Mémoire sur les fonctions fuchsiennes, Acta Math. 1 (1882), no. 1, 193–294 (French). MR 1554584, DOI 10.1007/BF02391845
Additional Information
- © Copyright 1973 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 181 (1973), 385-400
- MSC: Primary 10D15
- DOI: https://doi.org/10.1090/S0002-9947-1973-0337791-2
- MathSciNet review: 0337791