Construction of automorphic forms and integrals

Niebur, Douglas

doi:10.1090/S0002-9947-1974-0344196-8

Construction of automorphic forms and integrals
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by Douglas Niebur

Trans. Amer. Math. Soc. 191 (1974), 373-385

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

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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.

References

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On the partition function

43

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