A note on the number of irrational odd zeta values, II
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866912184023384064 |
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| author | Lai, Li |
| author_facet | Lai, Li |
| contents | We prove that there are at least $1.284 \cdot \sqrt{s/\log s}$ irrational numbers among $ζ(3)$, $ζ(5)$, $ζ(7)$, $\ldots$, $ζ(s-1)$ 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). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_05321 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A note on the number of irrational odd zeta values, II Lai, Li Number Theory 11J72 (primary), 11M06, 33C20 (secondary) We prove that there are at least $1.284 \cdot \sqrt{s/\log s}$ irrational numbers among $ζ(3)$, $ζ(5)$, $ζ(7)$, $\ldots$, $ζ(s-1)$ 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). |
| title | A note on the number of irrational odd zeta values, II |
| topic | Number Theory 11J72 (primary), 11M06, 33C20 (secondary) |
| url | https://arxiv.org/abs/2501.05321 |