A Universal Bound on the Weil Functional and Its Violation Under a Displaced Zero

v1.2 update: Added Lemma 2.1 (unconditional prime bound) proving |W_primes| ≤ C₀(σ) = 10.593 via |cos| ≤ 1, independent of γ₀ and independent of RH. Remark 3.3 updated citing Rudnick-Sarnak (1996) and Garrett (2014) confirming the Guinand-Weil explicit formula is unconditional. The argument is now fully unconditional: no step invokes RH. C₀(σ=0.025) corrected to 10.593 (computed with p ≤ 10⁵). Manuscript expanded to 5 pages.

Authors

Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-06-12
DOI
https://doi.org/10.5281/zenodo.20672126
Primary Topic
Analytic Number Theory Research
Type
preprint
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preprint

A Universal Bound on the Weil Functional and Its Violation Under a Displaced Zero

Ariel Fernando Martini
Zenodo (CERN European Organization for Nuclear Research)
Analytic Number Theory Research
preprint

A Universal Bound on the Weil Functional and Its Violation Under a Displaced Zero

Ariel Fernando Martini
preprint en

Abstract

v1.2 update: Added Lemma 2.1 (unconditional prime bound) proving |W_primes| ≤ C₀(σ) = 10.593 via |cos| ≤ 1, independent of γ₀ and independent of RH. Remark 3.3 updated citing Rudnick-Sarnak (1996) and Garrett (2014) confirming the Guinand-Weil explicit formula is unconditional. The argument is now fully unconditional: no step invokes RH. C₀(σ=0.025) corrected to 10.593 (computed with p ≤ 10⁵). Manuscript expanded to 5 pages.

Zenodo (CERN European Organization for Nuclear Research)
Peace, Justice and strong institutions, Reduced inequalities
Analytic Number Theory Research
DOIOpen Access PDFOpenAlex
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A Universal Bound on the Weil Functional and Its Violation Under a Displaced Zero — Ariel Fernando Martini · Zenodo (CERN European Organization for Nuclear Research) (2026) | TGRS Research Map | TGRS