On counterexamples to the Mertens conjecture

2025/02/28 by Kim, Seungki, Nguyen, Phong Q. · 1 citation
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2502.21021

Abstract

We use state-of-art lattice algorithms to improve the upper bound on the lowest counterexample to the Mertens conjecture to ≈ exp(1.96 × 10¹⁹), which is significantly below the conjectured value of ≈ exp(5.15 × 10²³) by Kotnik and van de Lune [KvdL04].

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