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

2025/01/09 by Li Lai, Lai, Li · 2 citations
Mathematics · #11J72 (primary) #11M06 #33C20 (secondary) #Advanced Mathematical Identities #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2501.05321

openalex publication_date 2025/01/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 upon the previous finding by a constant factor. The proof combines the elimination technique of Fischler-Sprang-Zudilin (2019) with the Φ_n factor method of Zudilin (2001).

Cited by

• Linear independence of values of Dirichlet L functions
• On the irrationality of certain p-adic zeta values

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