OP-5740Status unassessedNumber theory

Irrationality of the Riemann zeta value at 11

TheoremDB P9602 · Candidate awaiting source review

Inferred from the community field; finer classification has not been reviewed.

Source candidate · not reviewedAs of 2026-09-08Source & evidence ↓

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Problem statement

Let $\zeta(s)$ denote the Riemann zeta function, defined for $\operatorname{Re}(s) > 1$ by $\zeta(s) = \sum_{n=1}^{\infty} n^{-s}$ and extended by analytic continuation to $\mathbb{C} \setminus \{1\}$ . Prove that $\zeta(11)$ is irrational.

Lean 4

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Formal statement

Lean 4

theorem irrational_eleven : ∃ x, Irrational x ∧ riemannZeta 11 = x

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Proofs & verification

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Progress & source assessment

Source-reported assessment, retrieved 8 September 2026. Frontier Science has not independently reviewed this status.

Open. No signed Lean verification is attached to this problem or its selected resolution.

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References

[1]TheoremDB P9602 link
[2]Source formal statement (not locally verified) link

Recorded progress

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Machine attempts

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Discussion

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