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The Negative Prolate Spectrum and the Riemann–Siegel Theta Function

Year: 2026

Type: article

Abstract: Connes and Moscovici found that the negative eigenvalues of the self-adjoint prolate wave operator reproduce the growth of the zeros of the Riemann zeta function. In the published version, their counting law for the associated Dirac operator contains a term −(log E)/2π. This paper proves that this term is absent. The proof is an elementary phase analysis, and it places the eigenvalues, up to O(t^{-2/3}), at the points where the Riemann–Siegel theta function equals (n − 3/8)π. LaTeX source, figure, PDF and a numerical check.

Source: Zenodo (CERN European Organization for Nuclear Research)

DOI: 10.5281/zenodo.24127213

Author: Bhattacharjee, Deep

Language: English

Topic: Analytic Number Theory Research

Subfield: Algebra and Number Theory

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W7225816670

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