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

Kannan Soundararajan; Maksym Radziwi{\l}{\l}

arxiv: 1509.06827 · v1 · pith:UOHYKKHJnew · submitted 2015-09-23 · 🧮 math.NT · math.CA

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

Maksym Radziwi{\l}{\l} , Kannan Soundararajan This is my paper

classification 🧮 math.NT math.CA

keywords tfraccentrallimitselbergtheoremzetaaccordingapproximately

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

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