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A class of nonanalytic automorphic functions

Published online by Cambridge University Press:  22 January 2016

Douglas Niebur
Douglas Niebur*
Affiliation:
Department of Mathematics, University of Maryland
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In this paper we consider a class of nonanalytic automorphic functions which were first mentioned to A. Selberg by C. L. Siegel. These functions have Fourier coefficients which are closely connected with the Fourier coefficients of analytic automorphic forms, and they are also eigenfunctions of the Laplace operator derived from the hyperbolic metric. We shall show how this latter property gives new results in the classical theory of automorphic forms.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 52 , December 1973 , pp. 133 - 145
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1973

References

[1] Erdélyi, A., et al., Higher Transcendental Functions, Vol. I, McGraw-Hill, New York, 1953.Google Scholar
[2] Erdélyi, A., Tables of Integral Transforms, Vol. I, McGraw-Hill, New York, 1954.Google Scholar
[3] Fok, V. A., On the representation of an arbitrary function by an integral involving Legendre’s functions with a complex index, C.R. (Dokl.) Acad. Sci. USSR, 39 (1943), 253–256.Google Scholar
[4] Kubota, T., Elementary theory of Eisenstein series, Kodansha LTD., Tokyo, 1973.Google Scholar
[5] Joseph, Lehner, Discontinuous groups and automorphic functions, American Mathematical Society, Providence, 1964.Google Scholar
[6] Selberg, A., Harmonic analysis and discontinuous groups in weakly symmetric riemannian spaces with applications to Dirichlet series, J. Indian Math. Soc, 20 (1956), 47–87.Google Scholar
[7] Watson, G. N., A Treatise on the Theory of Bessel Functions, Second edition, Cambridge University Press, Cambridge, 1952.Google Scholar