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arXiv:2107.13636 [math.NT]AbstractReferencesReviewsResources

A note on the mean values of the derivatives of $ζ'/ζ$

Andrés Chirre

Published 2021-07-28Version 1

Assuming the Riemann hypothesis, we obtain a formula for the mean value of the $k$-derivative of $\zeta'/\zeta$, depending on the pair correlation of zeros of the Riemann zeta-function. This formula allows us to obtain new equivalences to Montgomery's pair correlation conjecture. This extends a result of Goldston, Gonek, and Montgomery where the mean value of $\zeta'/\zeta$ was considered.

Categories: math.NT
Subjects: 11M06, 11M26
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