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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

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


Author: Audrey A. Terras
Journal: Trans. Amer. Math. Soc. 183 (1973), 477-486
MSC: Primary 10H10
MathSciNet review: 0323735
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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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DOI: http://dx.doi.org/10.1090/S0002-9947-1973-0323735-6
PII: S 0002-9947(1973)0323735-6
Keywords: Epstein zeta function, Chowla-Selberg formula, functional equation, Bessel functions, Dedekind $ \eta $-function, Kronecker limit formula
Article copyright: © Copyright 1973 American Mathematical Society