A note on the number of irrational odd zeta values, II

Abstract

We prove that there are at least $1.284\cdot \sqrt{s/\log s}$ irrational numbers among $\zeta (3)$, $\zeta (5)$, $\zeta (7)$, $\dots$, $\zeta (s-1)$ for any sufficiently large even integer $s$. This result improves upon the previous finding by a constant factor. The proof combines the elimination technique of Fischler-Sprang-Zudilin (2019) with the ${\Phi }_n$ factor method of Zudilin (2001).

17 pages, 1 table. v2 added a new observation (Rmk. 3.6) and improved the final constant