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A weighted central limit theorem for $\log|ζ(1/2+it)|$ (1912.08127v2)

Published 17 Dec 2019 in math.NT

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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