A weighted central limit theorem for $\log|\zeta(1/2+it)|$

Alessandro Fazzari

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arXiv · 1912.08127

A weighted central limit theorem for $\log|\zeta(1/2+it)|$

Alessandro Fazzari

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Abstract

Under the Riemann Hypothesis, we show that as $t$ varies in $T\leq t \leq 2T$, the distribution of $\log|\zeta(1/2+it)|$ with respect to the measure $|\zeta(1/2+it)|^2dt$ is approximately normal with mean $\log\log T$ and variance $\frac{1}{2}\log\log T$.

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Alessandro Fazzari. 2019-12-17. A weighted central limit theorem for $\log|\zeta(1/2+it)|$. https://arxiv.org/abs/1912.08127

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