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

2021/06/06 by C. P. Hughes, Hughes, Christopher, Andrew Pearce‐Crump +1 · 1 citation
Mathematics · #Analytic Number Theory Research #Meromorphic and Entire Functions #Advanced Mathematical Identities

paper · doi:10.48550/arxiv.2106.03005

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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• Integer moments of the derivatives of the Riemann zeta function

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