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An estimate of the second moment of a sampling of the Riemann zeta function on the critical line (1606.01179v1)

Published 3 Jun 2016 in math.CA

Abstract: We investigate the second moment of a random sampling $\zeta(1/2+iX_t)$ of the Riemann zeta function on the critical line. Our main result states that if $X_t$ is an increasing random sampling with gamma distribution, then for all sufficiently large $t$, [\mathbb{E} |\zeta(1/2+iX_t)|2 = \log t + O(\sqrt{\log t}\log\log t).]

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