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September 2011 Asymptotics of Keiper-Li coefficients
Juan Arias de Reyna
Funct. Approx. Comment. Math. 45(1): 7-21 (September 2011). DOI: 10.7169/facm/1317045228

Abstract

We show that the Riemann Hypothesis is equivalent to the assertion $(y_m)\in\ell_2$ where $y_m$ is defined by \[ \lambda_m=\frac12(\log m+\gamma-\log(2\pi)-1)+y_m, \] and $m\lambda_m$ represents the numbers in Xian-Jin Li's criterion. This confirms and further sharpens a conjecture of J. B. Keiper. We also present some other hypotheses equivalent to the Riemann Hypothesis.

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Juan Arias de Reyna. "Asymptotics of Keiper-Li coefficients." Funct. Approx. Comment. Math. 45 (1) 7 - 21, September 2011. https://doi.org/10.7169/facm/1317045228

Information

Published: September 2011
First available in Project Euclid: 26 September 2011

zbMATH: 1243.11086
MathSciNet: MR2865409
Digital Object Identifier: 10.7169/facm/1317045228

Subjects:
Primary: 11M26
Secondary: 11M06

Rights: Copyright © 2011 Adam Mickiewicz University

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Vol.45 • No. 1 • September 2011
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