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A note on the number of irrational odd zeta values, II
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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).
Forward citations
Cited by 2 Pith papers
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On the irrationality of certain $p$-adic zeta values
For every prime p ≥ 5, some p-adic zeta value ζ_p(i) with odd i ≤ p + p/log p + 5 is irrational.
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Multiple Zeta Values
An extensive expository survey of multiple zeta values, their finite/symmetric and q-analogue variants, and their modular-form connections, proving no new theorem.
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