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Transactions of the American Mathematical Society

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



Identities involving the coefficients of a class of Dirichlet series. V, VI

Author: Bruce C. Berndt
Journal: Trans. Amer. Math. Soc. 160 (1971), 157-167
MSC: Primary 30.24; Secondary 10.00
MathSciNet review: 0280693
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Abstract: In 1949 Chowla and Selberg gave a very useful formula for the Epstein zeta-function associated with a positive definite binary quadratic form. Several generalizations of this formula are given here. The method of proof is new and is based on a theorem that we formerly proved for ``generalized'' Dirichlet series. An easy proof of Kronecker's second limit formula is also given.

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Keywords: Epstein zeta-function, Chowla-Selberg formula, functional equation with gamma factors, "generalized'' Dirichlet series, identities
Article copyright: © Copyright 1971 American Mathematical Society