A weighted central limit theorem for $\log|\zeta(1/2+it)|$

Alessandro Fazzari

A weighted central limit theorem for $\log|\zeta(1/2+it)|$

Number Theory 2021-01-21 v2

Authors: Alessandro Fazzari

Abstract

Under the Riemann Hypothesis, we show that as $t$ varies in $T\leq t \leq 2T$ , the distribution of $\log|\zeta(1/2+it)|$ with respect to the measure $|\zeta(1/2+it)|^2dt$ is approximately normal with mean $\log\log T$ and variance $\frac{1}{2}\log\log T$ .

Keywords

central limit theorem riemann zeta function riemann hypothesis weighted measure normal distribution

Cite

@article{arxiv.1912.08127,
  title  = {A weighted central limit theorem for $\log|\zeta(1/2+it)|$},
  author = {Alessandro Fazzari},
  journal= {arXiv preprint arXiv:1912.08127},
  year   = {2021}
}

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18 pages

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