A note on the mean values of the derivatives of 𝜁’/𝜁

Chirre, Andrés

doi:10.1090/proc/15906

A note on the mean values of the derivatives of $\zeta ’/\zeta$
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Proc. Amer. Math. Soc. 150 (2022), 3253-3265 Request permission

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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