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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 is approximately normally distributed with mean 0 and variance log log .
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Maksym Radziwiłł, Kannan Soundararajan, Selberg’s central limit theorem for log . Enseign. Math. 63 (2018), no. 1, pp. 1–19