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

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: 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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