Statistic of zeros of Riemann auxiliary function

J. Arias de Reyna

Statistic of zeros of Riemann auxiliary function

Number Theory 2024-07-23 v2

Authors: J. Arias de Reyna

Abstract

We have computed all zeros $\beta+i\gamma$ of $\mathop{\mathcal R }(s)$ with $0<\gamma<215946.3$ . 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 $\beta<1/2$ .

Keywords

Riemann zeta function zeros statistical analysis beta value numerical computation

Cite

@article{arxiv.2406.03041,
  title  = {Statistic of zeros of Riemann auxiliary function},
  author = {J. Arias de Reyna},
  journal= {arXiv preprint arXiv:2406.03041},
  year   = {2024}
}

Comments

17 pages, 18 figures. Added links to the papers in arXiv. Added line of seeds to Figure 2 "Rzeta200.pdf" and substitute Figure 18 "RzetaCompletadaBWW.pdf" by a correct one

Statistic of zeros of Riemann auxiliary function

Abstract

Keywords

Cite

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