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On the joint second moment of zeta and its logarithmic derivative

Volume 217 / 2025

Alessandro Fazzari Acta Arithmetica 217 (2025), 379-394 MSC: Primary 11M06; Secondary 11M26 DOI: 10.4064/aa240531-6-10 Published online: 13 January 2025

Abstract

Assuming the Riemann Hypothesis, Goldston, Gonek and Montgomery (2001) studied the second moment of the log-derivative of $\zeta $ 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 $|\zeta (\frac{1}{2}+it)|^2$. 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.

Authors

  • Alessandro FazzariDépartement de mathématiques et de statistique
    Université de Montréal
    Montréal, QC H3C 3J7, Canada
    e-mail

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