Year: 2026
Type: preprint
Abstract: Recently, OpenAI announced a uniform $7/8$ zero-free half-plane for finite-order Hecke $L$-functions over $\mathbb{Q}(\sqrt{-3})$, together with its transfer to Dirichlet $L$-functions. Assuming the analytic inputs of that work, we improve the boundary from $7/8=0.875$ to $8748867/10000000=0.8748867$ for the same families. The improvement combines a relaxed direct estimate with an amplified first moment of the reflected numerator, obtained from the existing fourth-moment estimate. A two-stage parameter argument yields the stated boundary without strengthening the inverse-moment estimate.
Source: arXiv (Cornell University)
Authors: Xu, Yuanda, Sang, Hejian
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7221767074