Bessel series expansions of the Epstein zeta function and the functional equation

Terras, Audrey A.

doi:10.1090/S0002-9947-1973-0323735-6

Bessel series expansions of the Epstein zeta function and the functional equation
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by Audrey A. Terras PDF

Trans. Amer. Math. Soc. 183 (1973), 477-486 Request permission

Abstract:

For the Epstein zeta function of an n-ary positive definite quadratic form, $n - 1$ generalizations of the Selberg-Chowla formula (for the binary case) are obtained. Further, it is shown that these $n - 1$ formulas suffice to prove the functional equation of the Epstein zeta function by mathematical induction. Finally some generalizations of Kronecker’s first limit formula are obtained.

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