Full Density of Zeta Zeros on the Critical Line via GUE Universality

We prove that 100% of the nontrivial zeros of \zeta(s) lie on the critical line in the density sense: N_0(T)/N(T) \to 1 as T \to \infty. The proof combines two results. Key results: 3 theorems / propositions. Maturity: Working Paper. Target venue: Annals of Mathematics. Part of The Latent research program. Related papers in this program: Unconditional Results, Universal.

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Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-06-27
DOI
https://doi.org/10.5281/zenodo.20956170
Primary Topic
Analytic Number Theory Research
Type
article
Field-Weighted Citation Impact
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article

Full Density of Zeta Zeros on the Critical Line via GUE Universality

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

Full Density of Zeta Zeros on the Critical Line via GUE Universality

Tamás Nagy
article en

Abstract

We prove that 100% of the nontrivial zeros of \zeta(s) lie on the critical line in the density sense: N_0(T)/N(T) \to 1 as T \to \infty. The proof combines two results. Key results: 3 theorems / propositions. Maturity: Working Paper. Target venue: Annals of Mathematics. Part of The Latent research program. Related papers in this program: Unconditional Results, Universal.

Zenodo (CERN European Organization for Nuclear Research)
Openalex Percentile: Top 2%
Analytic Number Theory Research
DOIOpen Access PDFOpenAlex
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Full Density of Zeta Zeros on the Critical Line via GUE Universality — Tamás Nagy · Zenodo (CERN European Organization for Nuclear Research) (2026) | TGRS Research Map | TGRS