On the zeros of the zeta function of one ternary quadratic form
type: Item
instance of: scholarly article
title: On the zeros of the zeta function of one ternary quadratic form
zbMATH Open document ID: 1270.11037
published in: Journal of Mathematical Sciences (New York)
publication date: 2012-11-29T00:00:00Z
review text: In this paper the author reports on his calculations about the zeros of the Epstein zeta function corresponding to sums of three squares. It suffices to consider zeros with nonnegative imaginary part. The computations carried by the author demonstrate that among all the roots with imaginary part not exceeding 160000, there are exactly 95794 of them whose real part is \(3/4\) and exactly 202634 of them whose real part is bigger than \(3/4\). In general, if \(C(T)\) is the number of such zeros with real part \(3/4\) and imaginary part not exceeding \(T\), then the computations of the author suggest that the ratio \(C(T)/T\) stabilizes near 0.6 as \(T\) increases. The author gives some heuristics on the distribution of zeros as well.
reviewed by: Emre Alkan
Mathematics Subject Classification ID: 11E45
zbMATH DE Number: 6111013
zbMATH Keywords: Epstein zeta function
zbMATH Keywords: zeros
author: N. V. Proskurin
MaRDI profile type: Publication
full work available at URL: s10958-012-0896-y
OpenAlex ID: W1968383769
cites work: Contributions to the theory of the Dirichlet \(L\)-series and the Epstein zeta-functions
cites work: AN EXAMPLE IN THE THEORY OF THE SPECTRUM OF A FUNCTION
cites work: Hardy's theorem for zeta-function of quadratic forms
DOI: 10.1007/S10958-012-0896-Y
description: scientific article; zbMATH DE number 6111013