A note on the number of irrational odd zeta values II

Abstract

We prove that there are at least 1 . 284 · s / log s irrational numbers among ζ ( 3 ) , ζ ( 5 ) , ζ ( 7 ) , ⋯ , ζ ( s - 1 ) for any sufficiently large even integer s . This result improves the constant of a previous work. The proof combines the elimination technique of Fischler–Sprang–Zudilin (2019) with the Φ n factor method of Zudilin (2001).