A note on the mean values of the derivatives of $\zeta'/\zeta$

Andrés Chirre

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arXiv · 2107.13636

A note on the mean values of the derivatives of $\zeta'/\zeta$

Andrés Chirre

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Abstract

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.

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Andrés Chirre. 2021-07-28. A note on the mean values of the derivatives of $\zeta'/\zeta$. https://arxiv.org/abs/2107.13636

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