Year: 2026
Type: preprint
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 $\mathbb{Q}$. As a corollary, $ζ(3)/π^4$ is irrational.
Source: arXiv (Cornell University)
Author: Lai, Li
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7220739133