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

Maksym Radziwiłł; Kannan Soundararajan

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arXiv · 1509.06827

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

Maksym Radziwiłł·Kannan Soundararajan

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Abstract

We present a new and simple proof of Selberg's central limit theorem, according to which $\log |\zeta(\tfrac 12 + it)|$ is approximately normally distributed with mean $0$ and variance $\tfrac 12 \log\log t$.

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Maksym Radziwiłł, Kannan Soundararajan. 2015-09-23. Selberg's central limit theorem for $\log |\zeta(\tfrac 12+it)|$. https://arxiv.org/abs/1509.06827

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