Linear relations of zeroes of the zeta-function

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 $\mathrm{lim\hspace{0.17em}sup}M(x)x^{-1\mathrm{/}2}\ge 1.6383$ and that $\mathrm{lim\hspace{0.17em}inf}M(x)x^{-1\mathrm{/}2}\le -1.6383$.