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arXiv · 2305.00345

A new upper bound on the smallest counterexample to the Mertens conjecture

John Rozmarynowycz·Seungki Kim
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Abstract

We report the finding of the new upper bound on the lowest positive integer $x$ for which the Mertens conjecture \begin{equation*} \left| \sum_{1 \leq n \leq x} \mu(n) \right| < \sqrt{x} \end{equation*} fails to hold: $x < \exp(1.017 \times 10^{29})$, an improvement over previously known $\exp(1.59 \times 10^{40})$ due to Kotnik and te Riele [7].

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John Rozmarynowycz, Seungki Kim. 2023-04-29. A new upper bound on the smallest counterexample to the Mertens conjecture. https://arxiv.org/abs/2305.00345

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