A note on the number of irrational odd zeta values II

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).

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Publication Details

Journal
Journal de Théorie des Nombres de Bordeaux
Published
2026-09-16
DOI
https://doi.org/10.5802/jtnb.1368
Primary Topic
Advanced Mathematical Identities
Type
article
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A note on the number of irrational odd zeta values II

Li Lai
Journal de Théorie des Nombres de Bordeaux
Advanced Mathematical Identities
article

A note on the number of irrational odd zeta values II

Li Lai
article en

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).

Journal de Théorie des Nombres de BordeauxVol. 38(2)
Xiamen University (CN)
Openalex Percentile: Top 94%
Advanced Mathematical Identities
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A note on the number of irrational odd zeta values II — Li Lai · Journal de Théorie des Nombres de Bordeaux (2026) | TGRS Research Map | TGRS