A family of deformations of the Riemann xi-function

We introduce a family of deformations of the Riemann xi-function endowed with two continuous parameters. We show that it has rich analytic structure and that its conjectural (mild) zero-free region for some fixed parameter is a sufficient condition for the Riemann hypothesis to hold for the Riemann zeta function.

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Publication Details

Journal
Tokyo Tech Research Repository (Tokyo Institute of Technology)
Published
2026-01-20
Primary Topic
Analytic and geometric function theory
Type
article
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article

A family of deformations of the Riemann xi-function

鈴木正俊, Masatoshi Suzuki
Tokyo Tech Research Repository (Tokyo Institute of Technology)
Analytic and geometric function theory
article

A family of deformations of the Riemann xi-function

鈴木正俊, Masatoshi Suzuki
article en

Abstract

We introduce a family of deformations of the Riemann xi-function endowed with two continuous parameters. We show that it has rich analytic structure and that its conjectural (mild) zero-free region for some fixed parameter is a sufficient condition for the Riemann hypothesis to hold for the Riemann zeta function.

Tokyo Tech Research Repository (Tokyo Institute of Technology)
Reduced inequalities
Openalex Percentile: Top 73%
Analytic and geometric function theory
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A family of deformations of the Riemann xi-function — 鈴木正俊, Masatoshi Suzuki · Tokyo Tech Research Repository (Tokyo Institute of Technology) (2026) | TGRS Research Map | TGRS