Linear relations of zeroes of the zeta-function

Abstract

This article considers linear relations between the non-trivial ze- roes of the Riemann zeta-function. The main application is an alternative disproof to Mertens’ conjecture by showing that lim supx→∞ M (x)x−1/2 ≥ 1.6383, and liminfx→∞ M(x)x−1/2 ≤ −1.6383. Show more