Non universality on the critical line

2012/07/20 by Johan Andersson, Andersson, Johan · 1 citation
Mathematics · #11M06 #Advanced Algebra and Geometry #Analytic Number Theory Research #FOS: Mathematics #Limits and Structures in Graph Theory #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1207.4927

openalex publication_date 2012/07/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove that the Riemann zeta-function is not universal on the critical line by using the fact that the Hardy Z-function is real, and some elementary considerations. This is a related to a recent result of Garunkstis and Steuding. We also prove conditional and partial results for non universality on the lines Re(s)=σfor 0

Citations

• On the value-distribution of the Riemann zeta-function on the critical line
• On generalized Hardy classes of Dirichlet series

Cited by

• On the Balasubramanian-Ramachandra method close to Re(s)=1

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