Statistic of zeros of Riemann auxiliary function

Abstract

We have computed all zeros ${\hat{I}}^2+i{\hat{I}}^3$ of $\mathcal{R}(s)$ with $0<{\hat{I}}^3<215946.3$. 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 ${\hat{I}}^2<1/2$.

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