zeta(3)的无理性指数的一个新上界
A new upper bound for the irrationality exponent of zeta(3)
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中文总结 AI 辅助
本文通过应用Rhin-Viola定理5.1于新的积分方向，将zeta(3)的无理性指数上界改进至5.5138800，优于此前保持25年的最佳结果，并指出Rhin-Viola点并非全局最优。
中文摘要 AI 辅助
我们证明了 $ζ(3)$ 的无理性指数满足 $μ(ζ(3)) < 5.5138800$，改进了 Rhin 和 Viola 在 2001 年得到的上界 $5.513891$，该上界在二十五年来一直是最佳已知结果。证明是对他们的定理 5.1 在一个新的积分方向上的应用。该方向并非通过扩大搜索范围达到：其八个参数是他们的 52000 倍，偏移量至多为 23。该机制是 Bai 最近用于 $π$ 的机制。特别是，Rhin-Viola 点在枚举覆盖的每个区域中都是最优的，但并非最优。
英文摘要
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.
