English

Selberg's central limit theorem for $\log |\zeta(\tfrac 12+it)|$

Number Theory 2015-09-24 v1 Classical Analysis and ODEs

Abstract

We present a new and simple proof of Selberg's central limit theorem, according to which logζ(12+it)\log |\zeta(\tfrac 12 + it)| is approximately normally distributed with mean 00 and variance 12loglogt\tfrac 12 \log\log t.

Keywords

Cite

@article{arxiv.1509.06827,
  title  = {Selberg's central limit theorem for $\log |\zeta(\tfrac 12+it)|$},
  author = {Maksym Radziwiłł and Kannan Soundararajan},
  journal= {arXiv preprint arXiv:1509.06827},
  year   = {2015}
}

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12 pages