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arXiv · 2610.06838

The linear independence of $1$, $ζ(3)$, and $ζ(4)$

Li Lai
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Abstract

In a recent breakthrough, Fauzan proved the irrationality of $ζ(5)$. In this paper, we combine Fauzan's determinant method with classical simultaneous approximations of zeta values studied by Zudilin and Dauguet--Zudilin to prove the linear independence of $1$, $ζ(3)$, and $ζ(4)$ over $\mathbb{Q}$.

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Li Lai. 2026-10-05. The linear independence of $1$, $ζ(3)$, and $ζ(4)$. https://arxiv.org/abs/2610.06838

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