Selberg's conjecture concerning the distribution of imaginary parts of zeros of the Riemann zeta function
type: Item
instance of: scholarly article
title: Selberg's conjecture concerning the distribution of imaginary parts of zeros of the Riemann zeta function
zbMATH Open document ID: 1221.11182
DOI: 10.1134/S1064562408040170
author: M. A. Korolev
published in: Doklady Mathematics
publication date: 2011-06-08T00:00:00Z
review text: Let \(\gamma_n\) denote the positive ordinates of zeros of the Riemann zeta function arranged in increasing order, \(t_n\) the Gramm points, \(\Delta_n=n-\nu\) with \(t_{\nu-1}<\gamma_n\leq t_\nu\). The author proves Selberg's conjecture: if \(\Phi(n)\) is a positive function of \(n\) tending to \(\infty\) then \[ \frac{\sqrt{\log\log n}}{\Phi(n)}<|\Delta_n|<\Phi(n)\sqrt{\log\log n} \] for almost all \(n\).
reviewed by: Florin Nicolae
Mathematics Subject Classification ID: 11M26
zbMATH DE Number: 5905416
zbMATH Keywords: Riemann zeta function
zbMATH Keywords: zeros
zbMATH Keywords: imaginary parts
zbMATH Keywords: Gramm points
zbMATH Keywords: Selberg's conjecture
Wikidata QID: Q123218935
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 5905416