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

preprint2015arXivOpen access

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

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

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Selberg's central limit theorem for log⁡∣ζ(12+it)∣\log |ζ(\tfrac 12+it)|log∣ζ(21​+it)∣

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