At least two of $\zeta(5),\zeta(7),\ldots,\zeta(35)$ are irrational

Li Lai; Li Zhou

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arXiv · 2103.00904

At least two of $\zeta(5),\zeta(7),\ldots,\zeta(35)$ are irrational

Li Lai·Li Zhou

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Abstract

Let $\zeta(s)$ be the Riemann zeta function. We prove the statement in the title, which improves a recent result of Rivoal and Zudilin by lowering $69$ to $35$. We also prove that at least one of $\beta(2),\beta(4),\ldots,\beta(10)$ is irrational, where $\beta(s) = L(s,\chi_4)$ and $\chi_4$ is the Dirichlet character with conductor $4$.

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Li Lai, Li Zhou. 2021-03-01. At least two of $\zeta(5),\zeta(7),\ldots,\zeta(35)$ are irrational. https://arxiv.org/abs/2103.00904

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