On counterexamples to the Mertens conjecture

Abstract

We use state-of-art lattice algorithms to improve the upper bound on the lowest counterexample to the Mertens conjecture to $\approx \exp (1.96\times 10^{19})$, which is significantly below the conjectured value of $\approx \exp (5.15\times 10^{23})$ by Kotnik and van de Lune [KvdL04].