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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)


Construction of automorphic forms and integrals

Author: Douglas Niebur
Journal: Trans. Amer. Math. Soc. 191 (1974), 373-385
MSC: Primary 10D15; Secondary 30A58
MathSciNet review: 0344196
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Abstract: It is well known that modular forms of positive dimension have Fourier coefficients given by certain infinite series involving Kloostermann sums and the modified Bessel function of the first kind. In this paper a functional equation which characterizes all such Fourier series is found. It is also shown that these Fourier series have a construction similar to that of Poincaré series of negative dimension.

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PII: S 0002-9947(1974)0344196-8
Keywords: Abelian integrals, Fourier coefficients of automorphic forms, Riemann-Roch theorem
Article copyright: © Copyright 1974 American Mathematical Society