Effective Weak Universality in Short Intervals

2024/03/04 by Saeree Wananiyakul, Wananiyakul, Saeree, Jörn Steuding +3 · 1 citation
Computer Science · Engineering · #11M06 (Primary) #11M26 #30E10 (Secondary) #Complex Variables (math.CV) #Control Systems and Identification #FOS: Mathematics #Neural Networks and Applications #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2403.01787

openalex publication_date 2024/03/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove an effective universality theorem of the Riemann zeta-function in short intervals [T,T+H] with T^(27)/(82)≤ H≤ T by following an effective multidimensional Ω-result of Voronin. Furthermore, we also prove the results in short intervals [T,T+H] with T^ε≤ H≤ T (for any fixed ε>0) under the assumption of the Riemann Hypothesis.

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• Effective hybrid joint universality for Dirichlet L-functions and its application

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