Quasi-Riemann hypothesis

The quantity is the zero-free half-plane threshold θ\theta for zeta, Dirichlet functions and finite-order Eisenstein Hecke functions over Q(−3)\mathbb{Q}(\sqrt{-3}). A lower threshold is better. The claims retain the source proof conditions.

OpenAI baseline: 7/87/8, released .

These results are Claimed: their authors published them, and we have not checked them.

BoundEvidence levelAuthorDateProof scope
≈0.874957019420099\approx0.874957019420099
Exact value and conditions
σ†\sigma^{\dagger}

Here σ†\sigma^{\dagger} is the root in (0.8749570194,0.8749570195)(0.8749570194,0.8749570195) of 7884s3−18819s2+14643s−3686=07884s^3-18819s^2+14643s-3686=0. The paper is conditional. The bound assumes the released Hecke analytic and transfer inputs and the retuned probe estimates in the linked written argument.

ClaimedJizhou Guo
Proof scope

Repository has Lean, but this result has exact-arithmetic certificates and a conditional paper.

10499/1200010499/12000ClaimedAkash Levy
Proof scope

228 new modules reported in source package.

≤0.87488664704\le0.87488664704
Exact value and conditions
11/12−ℓ/411/12-\ell/4

Here ℓ\ell is the unique root in [1/6,1/5][1/6,1/5] of 927ℓ4−3135ℓ3+2433ℓ2+275ℓ−100=0927\ell^4-3135\ell^3+2433\ell^2+275\ell-100=0. The certified display upper bound is 683505193/781250000683505193/781250000.

ClaimedHailey Collet
Proof scope

Proof contribution and reported multi-kernel receipts.

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