PreprintCC BY 4.0arXiv
Amplified moments and a refinement of the quasi-Riemann hypothesis
Abstract
Recently, OpenAI announced a uniform 7/8 zero-free half-plane for finite-order Hecke L-functions over ℚ(√(−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.
Related
- Some applications of the quasi-Riemann hypothesis to class groups and small generators of number fields
- Improved zero-free half-planes for the quasi-Riemann hypothesis
- Zero-free half-planes for Hecke L-functions over number fields and Quasi-Riemann Hypothesis
- Currently, there are no reasons to doubt the Riemann Hypothesis: The zeta function beyond the realm of computation
- A Formal Proof of Riemann Hypothesis from Existence Alone, the Sign Excepted by Theorem: The Constructed Witness, the Identity Cone over the Fixed Locus, the Grounded Counter-Model, and the Cure Theorem Proved in Lean 4 and Re-executed in Fortran
BibTeX
@misc{xu2026amplified,
title = {{Amplified moments and a refinement of the quasi-Riemann hypothesis}},
author = {Yuanda Xu and Hejian Sang},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.15291},
eprint = {2610.15291},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.15291},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Amplified moments and a refinement of the quasi-Riemann hypothesis
AU - Yuanda Xu
AU - Hejian Sang
PY - 2026
DA - 2026/10/15
PB - arXiv
DO - 10.48550/arxiv.2610.15291
UR - https://arxiv.org/abs/2610.15291
AB - Recently, OpenAI announced a uniform 7/8 zero-free half-plane for finite-order Hecke L-functions over ℚ(√(−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.
ER -