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A note on the mean values of the derivatives of $\zeta'/\zeta$
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classification
math.NT
keywords
zetameancorrelationformulamontgomeryobtainpairriemann
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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