Joint value-distribution of shifts of the Riemann zeta-function

2020/10/16 by Łukasz Pańkowski, Pańkowski, Łukasz
Mathematics · #Advanced Differential Equations and Dynamical Systems #FOS: Mathematics #Mathematical Dynamics and Fractals #Meromorphic and Entire Functions #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2010.08332

openalex publication_date 2020/10/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove that any non-zero complex values z₁,…,z_n can be approximated by the following integral shifts of the Riemann zeta-function ζ(s+id₁τ),…,ζ(s+id_nτ) for infinitely many τ, provided d₁,…,d_n∈ℕ and s is a fixed complex number lying in the right open half of the critical strip.

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