A sharp three-point kernel bound and improved proportions of zeta zeros

We prove that the auxiliary ratio in Wang's three-point kernel argument has sharp maximum sqrt(2), attained exactly at (0,1) and (1,0). Substitution into the source-pinned framework of arXiv:2609.24167v1 gives a lower proportion 0.6725007995946757558... of nontrivial zeta zeros that are simple and on the critical line, with a distinct-zero companion 0.8362503997973378779.... Directed rational intervals and an independent 120-decimal interval replay certify the numerical comparisons. The global transfer depends on a recent unreviewed preprint. The result is asymptotic and does not prove the Riemann hypothesis.

Authors

Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-09-24
DOI
https://doi.org/10.5281/zenodo.22940291
Primary Topic
Analytic Number Theory Research
Type
preprint
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preprint

A sharp three-point kernel bound and improved proportions of zeta zeros

Felipe A. Santibáñez-Leal
Zenodo (CERN European Organization for Nuclear Research)
Analytic Number Theory Research
preprint

A sharp three-point kernel bound and improved proportions of zeta zeros

Felipe A. Santibáñez-Leal
preprint en

Abstract

We prove that the auxiliary ratio in Wang's three-point kernel argument has sharp maximum sqrt(2), attained exactly at (0,1) and (1,0). Substitution into the source-pinned framework of arXiv:2609.24167v1 gives a lower proportion 0.6725007995946757558... of nontrivial zeta zeros that are simple and on the critical line, with a distinct-zero companion 0.8362503997973378779.... Directed rational intervals and an independent 120-decimal interval replay certify the numerical comparisons. The global transfer depends on a recent unreviewed preprint. The result is asymptotic and does not prove the Riemann hypothesis.

Zenodo (CERN European Organization for Nuclear Research)
Analytic Number Theory Research
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A sharp three-point kernel bound and improved proportions of zeta zeros — Felipe A. Santibáñez-Leal · Zenodo (CERN European Organization for Nuclear Research) (2026) | TGRS Research Map | TGRS