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Statistic of zeros of Riemann auxiliary function (2406.03041v2)
Published 5 Jun 2024 in math.NT
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 $\beta<1/2$.
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