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

Li Lai

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

Number Theory 2025-01-14 v2

Authors: Li Lai

Abstract

We prove that there are at least $1.284 \cdot \sqrt{s/\log s}$ irrational numbers among $\zeta(3)$ , $\zeta(5)$ , $\zeta(7)$ , $\ldots$ , $\zeta(s-1)$ 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).

Keywords

irrational odd zeta values zeta(3) zeta(5) elimination technique Phi_n factor method lower bound

Cite

@article{arxiv.2501.05321,
  title  = {A note on the number of irrational odd zeta values, II},
  author = {Li Lai},
  journal= {arXiv preprint arXiv:2501.05321},
  year   = {2025}
}

Comments

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

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

Abstract

Keywords

Cite

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