A discrete mean-value theorem for the higher derivatives of the Riemann zeta function

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JournalJournal of Number Theory
DateAccepted/In press - 4 Mar 2022
Number of pages23
Original languageEnglish

Abstract

We show that the nth derivative of the Riemann zeta function, when summed over the non-trivial zeros of zeta, is real and positive/negative in the mean for n odd/even, respectively. We show this by giving a full asymptotic expansion of these sums.

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