Critical Liouville Energies and Zeta-Zero Detection

A multipole theorem bounds the normalized Liouville energy from below by a sum of pole contributions. A positive Fejer weight and a certified finite calculation give an unconditional limsup lower bound strictly greater than 1811/2500. RH and Dirichlet GRH remain open.

Authors

Deep Bhattacharjee (ORCID: https://orcid.org/0000-0003-0466-750X)
Ushashi Bhattacharya (ORCID: https://orcid.org/0009-0002-2254-3914)

Institutions

University of Calcutta (IN)
National Taiwan University (TW)

Publication Details

Journal: Zenodo (CERN European Organization for Nuclear Research)
Published: 2026-11-07
DOI: https://doi.org/10.5281/zenodo.24014164
Primary Topic: Analytic Number Theory Research
Type: preprint

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preprint

Critical Liouville Energies and Zeta-Zero Detection

Deep Bhattacharjee, Ushashi Bhattacharya

Nov 7, 2026

4 links

Zenodo (CERN European Organization for Nuclear Research)

Analytic Number Theory Research

preprint

Critical Liouville Energies and Zeta-Zero Detection

Deep Bhattacharjee, Ushashi Bhattacharya

November 7, 2026preprint en

Abstract

Zenodo (CERN European Organization for Nuclear Research)

University of Calcutta (IN), National Taiwan University (TW)

Analytic Number Theory Research

DOI Open Access PDF OpenAlex

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Critical Liouville Energies and Zeta-Zero Detection — Deep Bhattacharjee, Ushashi Bhattacharya · Zenodo (CERN European Organization for Nuclear Research) (2026) | TGRS Research Map | TGRS