Statistic of zeros of Riemann auxiliary function

2024/06/05 by Juan Arias de Reyna, de Reyna, J. Arias
Mathematics · #Differential Equations and Boundary Problems #FOS: Mathematics #Meromorphic and Entire Functions #Number Theory (math.NT) #Primary 11M06 #Secondary 30D99 #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.2406.03041

openalex publication_date 2024/06/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We have computed all zeros β+iγ of \mathop\mathcal R (s) with 0<γ<215946.3. A total of 162215 zeros with 25 correct decimal digits. In this paper we offer some statistic based on this set of zeros. Perhaps the main interesting result is that 63.9% of these zeros satisfies β<1/2.

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