Linear relations of zeroes of the zeta-function

Darcy Best; Tim Trudgian

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arXiv · 1209.3843

Linear relations of zeroes of the zeta-function

Darcy Best·Tim Trudgian

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Abstract

This article considers linear relations between the non-trivial zeroes of the Riemann zeta-function. The main application is an alternative disproof to Mertens' conjecture. We show that $\limsup M(x)x^{-1/2} \geq 1.6383$ and that $\liminf M(x)x^{-1/2}\leq -1.6383$.

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Darcy Best, Tim Trudgian. 2012-09-18. Linear relations of zeroes of the zeta-function. https://arxiv.org/abs/1209.3843

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