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

v1.3 update: Added Lemma 2.2 (archimedean bound) computing |W_arch| ≤ C₁ = 0.146 via Stirling expansion of Re[ψ(¼+iτ/2)], verified numerically with scipy.special.digamma for γ₀ ∈ [14, 10¹⁰]. Corrects Gemini's overestimate by factor 16x. Total bound: C_total = C₀ + C₁ = 10.739. Safety factor: 2980/10.739 = 277x. Both Lemma 2.1 and Lemma 2.2 are fully unconditional.

Authors

Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-06-12
DOI
https://doi.org/10.5281/zenodo.20672354
Primary Topic
Polynomial and algebraic computation
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)
Polynomial and algebraic computation
preprint

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

Ariel Fernando Martini
preprint en

Abstract

v1.3 update: Added Lemma 2.2 (archimedean bound) computing |W_arch| ≤ C₁ = 0.146 via Stirling expansion of Re[ψ(¼+iτ/2)], verified numerically with scipy.special.digamma for γ₀ ∈ [14, 10¹⁰]. Corrects Gemini's overestimate by factor 16x. Total bound: C_total = C₀ + C₁ = 10.739. Safety factor: 2980/10.739 = 277x. Both Lemma 2.1 and Lemma 2.2 are fully unconditional.

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