On Li's criterion for the Riemann hypothesis for the Selberg class
type: Item
instance of: scholarly article
title: On Li's criterion for the Riemann hypothesis for the Selberg class
zbMATH Open document ID: 1188.11046
published in: Journal of Number Theory
publication date: 2010-04-08T00:00:00Z
review text: The author proves a generalization of Li's positivity criterion for the Riemann hypothesis for the extended Selberg class with an Euler sum and obtains two arithmetic expressions for Li's coefficients \(\lambda_F(n)=\sum_\rho\left(1-\left(1-\frac{1}{\rho}\right)^n\right) \) of a function \(F\), where the sum is taken over all non-trivial zeros of \(F\). For related research see \textit{S. Omar} and \textit{K. Mazhouda} [J. Number Theory 125, No. 1, 50--58 (2007; Zbl 1137.11060), J. Number Theory 130, No. 4, 1098--1108 (2010; Zbl 1188.11044), J. Number Theory 130, No. 4, 1109--1114 (2010; Zbl 1188.11045)].
reviewed by: Florin Nicolae
Mathematics Subject Classification ID: 11M41
Mathematics Subject Classification ID: 11M26
zbMATH DE Number: 5690722
zbMATH Keywords: Selberg class
zbMATH Keywords: Riemann hypothesis
zbMATH Keywords: Li's criterion
author: Lejla Smajlovic
MaRDI profile type: Publication
full work available at URL: j.jnt.2009.10.012
OpenAlex ID: W1968199770
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DOI: 10.1016/J.JNT.2009.10.012
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description: scientific article; zbMATH DE number 5690722