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
DOI:
https://doi.org/10.1090/S0002-9947-1973-0323735-6
MathSciNet review:
0323735
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Abstract | References | Similar Articles | Additional Information
Abstract: For the Epstein zeta function of an n-ary positive definite quadratic form, generalizations of the Selberg-Chowla formula (for the binary case) are obtained. Further, it is shown that these
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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Additional Information
DOI:
https://doi.org/10.1090/S0002-9947-1973-0323735-6
Keywords:
Epstein zeta function,
Chowla-Selberg formula,
functional equation,
Bessel functions,
Dedekind -function,
Kronecker limit formula
Article copyright:
© Copyright 1973
American Mathematical Society