Linear relations of zeroes of the zeta-function

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 $\mathrm{limsup}M(x)x^{-1/2}\ge 1.6383$ and that $\mathrm{liminf}M(x)x^{-1/2}\le -1.6383$.

12 pages, 2 figures, 2 tables. Version 2: some typos corrected. To appear in Math. Comp