A Complete Proof of the Riemann Hypothesis via Contradictions in Prime Fluctuations, Zero Density, and De Bruijn–Newman Dynamics

This paper presents a complete and unconditional proof of the Riemann Hypothesis (RH), showing that all non-trivial zeros of the Riemann zeta function lie on the critical line Re(s) = 1/2. The proof uses a contradiction framework constructed across three independent analytic domains: prime fluctuations, zero density estimates, and the dynamics of the De Bruijn–Newman constant Λ. No unproven conjectures are used. All arguments rely on known results in analytic number theory. This version is public for open peer review.

Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2025-03-24
DOI
https://doi.org/10.5281/zenodo.15079158
Primary Topic
Analytic Number Theory Research
Type
article
Field-Weighted Citation Impact
0.00
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article

A Complete Proof of the Riemann Hypothesis via Contradictions in Prime Fluctuations, Zero Density, and De Bruijn–Newman Dynamics

Zenodo (CERN European Organization for Nuclear Research)
Analytic Number Theory Research
article

A Complete Proof of the Riemann Hypothesis via Contradictions in Prime Fluctuations, Zero Density, and De Bruijn–Newman Dynamics

article en

Abstract

This paper presents a complete and unconditional proof of the Riemann Hypothesis (RH), showing that all non-trivial zeros of the Riemann zeta function lie on the critical line Re(s) = 1/2. The proof uses a contradiction framework constructed across three independent analytic domains: prime fluctuations, zero density estimates, and the dynamics of the De Bruijn–Newman constant Λ. No unproven conjectures are used. All arguments rely on known results in analytic number theory. This version is public for open peer review.

Zenodo (CERN European Organization for Nuclear Research)
Reduced inequalities
Openalex Percentile: Top 43%
Analytic Number Theory Research
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A Complete Proof of the Riemann Hypothesis via Contradictions in Prime Fluctuations, Zero Density, and De Bruijn–Newman Dynamics · Zenodo (CERN European Organization for Nuclear Research) (2025) | TGRS Research Map | TGRS