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

Author:

Terras Audrey A.

Abstract

For the Epstein zeta function of an n-ary positive definite quadratic form, n 1 n - 1 generalizations of the Selberg-Chowla formula (for the binary case) are obtained. Further, it is shown that these n 1 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.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Reference15 articles.

1. National Bureau of Standards Applied Mathematics Series, No. 55;Abramowitz, Milton,1964

2. On a certain function analogous to 𝑙𝑜𝑔_{𝜂}(𝑧);Asai, Tetsuya;Nagoya Math. J.,1970

3. On Epstein’s zeta function;Bateman, P. T.;Acta Arith.,1964

4. Identities involving the coefficients of a class of Dirichlet series. V, VI;Berndt, Bruce C.;Trans. Amer. Math. Soc. 160 (1971), 139-156; ibid.,1971

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