JournalslemVol. 63, No. 1/2pp. 1–19

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

  • Maksym Radziwiłł

    McGill University, Montreal, Canada
  • Kannan Soundararajan

    Stanford University, USA
Selberg’s central limit theorem for log $|\zeta(\tfrac 12+it)|$ cover

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Abstract

We present a new and simple proof of Selberg's central limit theorem, according to which the logarithm of the Riemann zeta-function at height tt is approximately normally distributed with mean 0 and variance 12\frac {1}{2} log log tt.

Cite this article

Maksym Radziwiłł, Kannan Soundararajan, Selberg’s central limit theorem for log ζ(12+it)|\zeta(\tfrac 12+it)|. Enseign. Math. 63 (2018), no. 1, pp. 1–19

DOI 10.4171/LEM/63-1/2-1