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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DOI:
http://dx.doi.org/10.1090/S0002-9947-1974-0344196-8

Keywords:
Abelian integrals,
Fourier coefficients of automorphic forms,
Riemann-Roch theorem

Article copyright:
© Copyright 1974
American Mathematical Society