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

v1.4 update: Remark 3.3 updated with explicit citation of Rudnick-Sarnak (1996), Proposition 2.1 (Duke Math. J. 81, no. 2, 269-322), confirming the Guinand-Weil explicit formula applies to Gaussian test functions analytic in |Im z| < 1/2+ε with rapid decay. References to Garrett (2014) added. The argument is now fully closed with all steps explicitly cited.

Authors

Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-06-12
DOI
https://doi.org/10.5281/zenodo.20672414
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

v1.4 update: Remark 3.3 updated with explicit citation of Rudnick-Sarnak (1996), Proposition 2.1 (Duke Math. J. 81, no. 2, 269-322), confirming the Guinand-Weil explicit formula applies to Gaussian test functions analytic in |Im z| < 1/2+ε with rapid decay. References to Garrett (2014) added. The argument is now fully closed with all steps explicitly cited.

Zenodo (CERN European Organization for Nuclear Research)
Reduced inequalities, Peace, Justice and strong institutions
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