Comparing zeros of distinct Dirichlet L-functions

2023/02/14 by William D. Banks, Banks, William D.
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.2302.07073

openalex publication_date 2023/02/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For any θ>\frac13, we show that there are constants c₁,c₂>0 that depend only on θ for which the following property holds. If χ₁,χ₂ are two distinct primitive Dirichlet characters modulo q, and T≥ c₁q^θ, then L(s,χ₁) and L(s,χ₂) do not have the same zeros in the region \s=σ+it∈\mathbb C:0<σ<1,~T\frac14.

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