On Fluctuations of Riemann's Zeta Zeros

Details On Fluctuations of Riemann's Zeta Zeros On Fluctuations of Riemann's Zeta Zeros

2012-03-23

arxiv.org/abs/1203.5309v1

Mathematics

Probability

23 pages

Scientific paper

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, \gamma_k and \gamma_{k+x}, with x asymptotically
equal to \alpha(\log k)^{\beta}, with \beta>0, for large k follow the
two-variate Gaussian distribution with correlation (1-\beta)_+.

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