Linear statistics for zeros of Riemann's zeta function

C. P. Hughes; Z. Rudnick

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Linear statistics for zeros of Riemann's zeta function

C. P. Hughes·Z. Rudnick

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Abstract

We consider a smooth counting function of the scaled zeros of the Riemann zeta function, around height T. We show that the first few moments tend to the Gaussian moments, with the exact number depending on the statistic considered.

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C. P. Hughes, Z. Rudnick. 2002-08-28. Linear statistics for zeros of Riemann's zeta function. https://arxiv.org/abs/math/0208220

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