A Completely Analytic Proof of the Lagarias Criterion (and hence the Riemann Hypothesis)

This revision (V19) replaces all remaining computational checks with fully analytic, symbolic arguments. In particular, the mid-range brute-force verification up to 101410^{14}1014 present in earlier versions has been entirely eliminated. All inequalities are now proven using closed-form analytic bounds and monotonicity lemmas, reducing the proof to a completely self-contained symbolic derivation. Appendix tables remain for transparency but are no longer necessary for logical completeness.

Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2025-07-18
DOI
https://doi.org/10.5281/zenodo.16228172
Primary Topic
Polynomial and algebraic computation
Type
article
Field-Weighted Citation Impact
0.00
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article

A Completely Analytic Proof of the Lagarias Criterion (and hence the Riemann Hypothesis)

Zenodo (CERN European Organization for Nuclear Research)
Polynomial and algebraic computation
article

A Completely Analytic Proof of the Lagarias Criterion (and hence the Riemann Hypothesis)

article en

Abstract

This revision (V19) replaces all remaining computational checks with fully analytic, symbolic arguments. In particular, the mid-range brute-force verification up to 101410^{14}1014 present in earlier versions has been entirely eliminated. All inequalities are now proven using closed-form analytic bounds and monotonicity lemmas, reducing the proof to a completely self-contained symbolic derivation. Appendix tables remain for transparency but are no longer necessary for logical completeness.

Zenodo (CERN European Organization for Nuclear Research)
Peace, Justice and strong institutions
Openalex Percentile: Top 52%
Polynomial and algebraic computation
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A Completely Analytic Proof of the Lagarias Criterion (and hence the Riemann Hypothesis) · Zenodo (CERN European Organization for Nuclear Research) (2025) | TGRS Research Map | TGRS