Abstract
We obtain a full asymptotic for the sum of [Formula: see text], where [Formula: see text] denotes the [Formula: see text]th derivative of the Riemann zeta function, [Formula: see text] is a positive real number, and [Formula: see text] denotes a nontrivial zero of the Riemann zeta function. The sum is over the zeros with imaginary parts up to a height [Formula: see text], as [Formula: see text]. We also specify what the asymptotic formula becomes when [Formula: see text] is a positive integer, highlighting the differences in the asymptotic expansions as [Formula: see text] changes its arithmetic nature.
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