Hermite-Biehler Reformulation for the Theta Kernel

Figshare 2026 Preprint Open access

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Authors: Angela Whitehead, Joshua Pereira
DOI: 10.6084/m9.figshare.31290559
Cited by: 0

Abstract

We record a de Branges/Hermite-Biehler (HB) reformulation of the cosine-kernel representation of Riemann’s completed function on the critical line. The note is conditional: it isolates a single HB certificate (equivalently, a Pick/Herglotz property of a boundary ratio) whose verification for the explicit theta-kernel would imply the Riemann Hypothesis. This paper is part 2 of 3

Fields of Study & Subjects

Analytic Number Theory Research Mathematical Analysis and Transform Methods Mathematical functions and polynomials

Publication details

Journal / source
Figshare
Publication date
1 January 2026
Document type
Preprint