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

Terras, A.

doi:10.1090/S0002-9947-1975-0369267-2

Fourier coefficients of Eisenstein series of one complex variable for the special linear group
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Trans. Amer. Math. Soc. 205 (1975), 97-114 Request permission

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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