The Generalized Riemann Hypothesis from zeros of the zeta function

2023/03/16 by William D. Banks, Banks, William D. · 1 citation
Mathematics · #11M06 #11M26 #Analytic Number Theory Research #Analytic and geometric function theory #FOS: Mathematics #Meromorphic and Entire Functions #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2303.09510

openalex publication_date 2023/03/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show that the Generalized Riemann Hypothesis for all Dirichlet L-functions is a consequence of certain conjectural properties of the zeros of the Riemann zeta function. Conversely, we prove that the zeros of ζ(s) satisfy those properties under GRH.

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• Detecting zeros of Dirichlet L-functions via the Riemann zeta-function

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