An effective universality theorem for the Riemann zeta function

2016/11/30 by Youness Lamzouri, Lamzouri, Youness, Stephen Lester +3 · 1 citation
Mathematics · #Algebraic Geometry and Number Theory #Analytic Number Theory Research #FOS: Mathematics #Limits and Structures in Graph Theory #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1611.10325

openalex publication_date 2016/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let 0 0, once T is large enough. This was refined by Bagchi who showed that the measure of such t ∈ [0,T] is (c(ε) + o(1)) T, for all but at most countably many ε > 0. Using a completely different approach, we obtain the first effective version of Voronin's Theorem, by showing that in the rate of convergence one can save a small power of the logarithm of T. Our method is flexible, and can be generalized to other L-functions in the t-aspect, as well as to families of L-functions in the conductor aspect.

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