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

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

12 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 sup_x→∞M(x)x^-1/2 ≥ 1.6383, and lim inf_x→∞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

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title = "Linear relations of zeroes of the zeta-function",

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.

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JO - Mathematics of Computation

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Linear relations of zeroes of the zeta-function

Abstract

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