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

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math.NT2026★ 5 cited

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

Christopher Hughes, Andrew Pearce-Crump

We show that the th derivative of the Riemann zeta function, when summed over the non-trivial zeros of zeta, is real and positive/negative in the mean for odd/even, respecti…

math.NT2024

A heuristic for discrete mean values of the derivative of the Riemann zeta function

Christopher Hughes, Greg Martin, Andrew Pearce-Crump

Shanks conjectured that , where ranges over non-trivial zeros of the Riemann zeta function, is real and positive in the mean. We present a history of this problem, i…