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December 2017 On a Class of Epstein Zeta Functions
Sami OMAR
Tokyo J. Math. 40(2): 339-351 (December 2017). DOI: 10.3836/tjm/1502179232

Abstract

X.-J.~Li gave in~[4] a criterion for the Riemann hypothesis in terms of the positivity of a set of coefficients. In this paper, we investigate exactly how the Li criterion for the Riemann hypothesis fails for a class of Epstein zeta functions. This enables to derive some interesting consequences regarding $c_K=\frac{h_K\log d_K}{\sqrt{d_K}}$ of a quadratic imaginary field $K$ of absolute discriminant $d_K$ and class number $h_K$. Similar results are stated for the period ratios of elliptic curves with complex multiplication.

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Sami OMAR. "On a Class of Epstein Zeta Functions." Tokyo J. Math. 40 (2) 339 - 351, December 2017. https://doi.org/10.3836/tjm/1502179232

Information

Published: December 2017
First available in Project Euclid: 9 January 2018

zbMATH: 06855939
MathSciNet: MR3743723
Digital Object Identifier: 10.3836/tjm/1502179232

Subjects:
Primary: 11M06
Secondary: 11M26, 11M36

Rights: Copyright © 2017 Publication Committee for the Tokyo Journal of Mathematics

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Vol.40 • No. 2 • December 2017
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