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arXiv · 2502.21021

On counterexamples to the Mertens conjecture

Seungki Kim·Phong Q. Nguyen
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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].

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BibTeXRIS

Seungki Kim, Phong Q. Nguyen. 2025-02-28. On counterexamples to the Mertens conjecture. https://arxiv.org/abs/2502.21021

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