A Scalar Deviation Measure for the Zeros of the Riemann Zeta Function
Henry Chan (Jung Hyo Chan) · 2026
We introduce the scalar deviation measure VRH := sup |Re(ρ) − 1/2| over the non-trivial zeros of the Riemann zeta function, establishing that the Riemann Hypothesis is equivalent to VRH = 0. We connect this measure to the De Bruijn–Newman constant Λ, showing VRH = 0 ⇔ Λ = 0, and derive explicit numerical bounds using Platt–Trudgian zero-free region results. No new results on RH are claimed; the contribution is a unified measurement framework.
arXiv Submission Pending
Paper B
A Quantitative Pole-Zero Exponent Inequality in the Guinand–Weil Explicit Formula
Henry Chan (Jung Hyo Chan) · 2026
Building on the VRH framework, this paper establishes quantitative results connecting the scalar deviation measure to the Guinand–Weil explicit formula, deriving both conditional and unconditional theorems.
Forthcoming
Research
This research programme develops scalar deviation measures for the zeros of the Riemann zeta function and related L-functions.
The central object is VRH := sup |Re(ρ) − 1/2|, a single non-negative scalar that quantifies how far the known zeros deviate from the critical line. The Riemann Hypothesis is equivalent to VRH = 0.
We do not claim to prove RH. We provide a framework for measuring it — connecting classical zero-free regions, the De Bruijn–Newman constant, and explicit formula methods into a unified quantitative picture.
About
Henry Chan (Jung Hyo Chan, 정효찬)
Independent Researcher · Seoul, Korea
Research interests: analytic number theory, scalar deviation measures, zero distribution of the Riemann zeta function, and connections to the De Bruijn–Newman constant.