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arXiv · 2609.26980

A new upper bound for the irrationality exponent of zeta(3)

David Niedbala Giraudin
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Abstract

We prove that the irrationality exponent of $ζ(3)$ satisfies $μ(ζ(3)) < 5.5138800$, improving the bound $5.513891$ obtained by Rhin and Viola in 2001, which has been the best known for twenty-five years. The proof is an application of their Theorem 5.1 at a new integral direction. That direction is not reached by enlarging the search range: its eight parameters are 52000 times theirs, shifted by at most 23. The mechanism is the one recently used by Bai for $π$. In particular the Rhin-Viola point, optimal in every region covered by enumeration, is not optimal.

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David Niedbala Giraudin. 2026-09-22. A new upper bound for the irrationality exponent of zeta(3). https://arxiv.org/abs/2609.26980

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