A note on the mean values of the derivatives of ζ/ζ
Peer reviewed, Journal article
Accepted version
Date
2022Metadata
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- Institutt for matematiske fag [2474]
- Publikasjoner fra CRIStin - NTNU [38294]
Original version
Proceedings of the American Mathematical Society. 2022, 150 (8), 3253-3265. 10.1090/proc/15906Abstract
Assuming the Riemann hypothesis, we obtain a formula for the mean value of the
-derivative of , 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 was considered.