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arXiv · 1511.06824

Zero-density estimates for Epstein zeta functions

Steven Gonek·Yoonbok Lee
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Abstract

We investigate the zeros of Epstein zeta functions associated with a positive definite quadratic form with rational coefficients in the vertical strip $ σ_1 < \Re s < σ_2 $, where $ 1/2 < σ_1 < σ_2 < 1 $. When the class number of the quadratic form is bigger than 1, Voronin gives a lower bound and Lee gives an asymptotic formula for the number of zeros. In this paper, we improve their results by providing a new upper bound for the error term.

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Steven Gonek, Yoonbok Lee. 2015-11-24. Zero-density estimates for Epstein zeta functions. https://arxiv.org/abs/1511.06824

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