A boundary product–certificate method for the Riemann zeta function: far-field zero-freeness, near-field energy barriers, and conditional closure of the Riemann Hypothesis

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Authors: Jonathan Washburn
Cited by: 0

Abstract

We prove that all nontrivial zeros of the Riemann zeta function with Re(s) >= 0.6 lie on the critical line (unconditional), and establish an effective zero-free barrier for the remaining strip with astronomical protection heights. Far-field (Re(s) >= 0.6): Unconditionally zero-free. The arithmetic Cayley field Θ is Schur (|Θ| ~ 10^8800. Main Result (Theorem 183). (a) (Unconditional) The Riemann zeta function has no zeros with Re(s) >= 0.6. (b) (Effective) No zeros with 1/2 < Re(s) < 0.6 exist at height |t|

Fields of Study & Subjects

Geometry and complex manifolds Spectral Theory in Mathematical Physics Algebraic Geometry and Number Theory

Publication details

Journal / source
Zenodo (CERN European Organization for Nuclear Research)
Publication date
2 January 2026
Document type
Preprint