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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Fourier coefficients of Eisenstein series of one complex variable for the special linear group


Author: A. Terras
Journal: Trans. Amer. Math. Soc. 205 (1975), 97-114
MSC: Primary 10D20; Secondary 10H10
DOI: https://doi.org/10.1090/S0002-9947-1975-0369267-2
MathSciNet review: 0369267
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Abstract: The Eisenstein series in question are generalizations of Epstein's zeta function, whose Fourier expansions generalize the formula of Selberg and Chowla (for the binary quadratic form case of Epstein's zeta function). The expansions are also analogous to Siegel's calculation of the Fourier coefficients of Eisenstein series for the symplectic group. The only ingredients not appearing in Siegel's formula are the Bessel functions of matrix argument studied by Herz. These functions generalize the modified Bessel function of the second kind appearing in the Selberg-Chowla formula.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1975-0369267-2
Keywords: Fourier coefficients, Eisenstein series, Epstein zeta function, special linear group, positive definite symmetric matrices, Bessel functions of matrix argument
Article copyright: © Copyright 1975 American Mathematical Society