Linear relations of zeroes of the zeta-function

D G Best; T S Trudgian

doi:10.1090/S0025-5718-2014-02916-5

Linear relations of zeroes of the zeta-function

D G Best, T S Trudgian

School of Mathematics

Research output: Contribution to journal › Article › Research › peer-review

11 Citations (Scopus)

Abstract

This article considers linear relations between the nontrivial zeroes of the Riemann zeta-function. The main application is an alternative disproof of Mertens' conjecture by showing that lim supx→∞M(x)x-1/2 ≥ 1.6383, and lim infx→∞M(x)x-1/2 ≤ -1.6383.

Original language	English
Pages (from-to)	2047-2058
Number of pages	12
Journal	Mathematics of Computation
Volume	84
Issue number	294
DOIs	https://doi.org/10.1090/S0025-5718-2014-02916-5
Publication status	Published - 2015

Keywords

Linear relations of ordinates
Riemann zeta-function zeros

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10.1090/S0025-5718-2014-02916-5

Cite this

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abstract = "This article considers linear relations between the nontrivial zeroes of the Riemann zeta-function. The main application is an alternative disproof of Mertens' conjecture by showing that lim supx→∞M(x)x-1/2 ≥ 1.6383, and lim infx→∞M(x)x-1/2 ≤ -1.6383.",

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AB - This article considers linear relations between the nontrivial zeroes of the Riemann zeta-function. The main application is an alternative disproof of Mertens' conjecture by showing that lim supx→∞M(x)x-1/2 ≥ 1.6383, and lim infx→∞M(x)x-1/2 ≤ -1.6383.

KW - Linear relations of ordinates

KW - Riemann zeta-function zeros

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DO - 10.1090/S0025-5718-2014-02916-5

M3 - Article

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VL - 84

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EP - 2058

JO - Mathematics of Computation

JF - Mathematics of Computation

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ER -

Linear relations of zeroes of the zeta-function

Abstract

Keywords

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