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arXiv · 2107.13636

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

Andrés Chirre
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Abstract

Assuming the Riemann hypothesis, we obtain a formula for the mean value of the $k$-derivative of $ζ'/ζ$, 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 $ζ'/ζ$ was considered.

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Andrés Chirre. 2022-01-03. A note on the mean values of the derivatives of $ζ'/ζ$. https://arxiv.org/abs/2107.13636

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