On the joint second moment of zeta and its logarithmic derivative

2023/10/24 by Alessandro Fazzari, Fazzari, Alessandro · 1 citation
Mathematics · #Analytic Number Theory Research #History and Theory of Mathematics #Advanced Mathematical Identities

paper · pdf · doi:10.48550/arxiv.2310.15918

Abstract

Assuming the Riemann Hypothesis, Goldston, Gonek and Montgomery \citeGGM studied the second moment of the log-derivative of ζ, shifted away from the half line by a/log T, and its connection with the pair correlation conjecture. In this paper, we consider a weighted version of this problem, where the average is tilted by |ζ((1)/(2)+it)|². More precisely, we provide an upper and a lower bound for the second moment of zeta times its logarithmic derivative, a/log T away from the critical line.

Cited by

• Selberg's Central Limit Theorem weighted by Linear Statistics of Zeta Zeros

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