Zero-density estimates for Epstein zeta functions

2015/11/21 by Steven Gonek, Gonek, Steven, Yoonbok Lee +1
Mathematics · #FOS: Mathematics #Number Theory (math.NT) #math.NT

paper · pdf · doi:10.48550/arxiv.1511.06824

arxiv created 2015/11/24 · arxiv updated 2015/11/25

Abstract

We investigate the zeros of Epstein zeta functions associated with a positive definite quadratic form with rational coefficients in the vertical strip σ₁ < \Re s < σ₂ , where 1/2 < σ₁ < σ₂ < 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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