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arXiv · 1203.5309

On Fluctuations of Riemann's Zeta Zeros

Vladislav Kargin
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Abstract

It is shown that the normalized fluctuations of Riemann's zeta zeros around their predicted locations follow the Gaussian law. It is also shown that fluctuations of two zeros, $γ_{k}$ and $γ_{k+x},$ with $x\sim(\log k)^β$, $β>0$, for large $k$ follow the two-variate Gaussian distribution with correlation $(1-β)_{+}$.

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Vladislav Kargin. 2014-07-18. On Fluctuations of Riemann's Zeta Zeros. https://doi.org/10.1007/s00440-012-0465-9

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