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

Maksym Radziwiłł; Kannan Soundararajan

doi:10.4171/lem/63-1/2-1

JournalslemVol. 63, No. 1/2pp. 1–19

Selberg’s central limit theorem for log $∣ ζ (\frac{1}{2} + i t) ∣$

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 $t$ is approximately normally distributed with mean 0 and variance $\frac{1}{2}$ log log $t$ .

Cite this article

Maksym Radziwiłł, Kannan Soundararajan, Selberg’s central limit theorem for log $∣ ζ (\frac{1}{2} + i t) ∣$ . Enseign. Math. 63 (2017), no. 1/2, pp. 1–19

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