Brent, RichardPlatt, David JohnTrudgian, Tim2023-02-270025-5718http://hdl.handle.net/1885/286464We consider sums of the form Σφ(γ), where φ is a given function, and γ ranges over the ordinates of nontrivial zeros of the Riemann zeta-function in a given interval. We show how the numerical estimation of such sums can be accelerated by a simple device, and give examples involving both convergent and divergent infinite sums.The second author was supported by ARC Grant DP160100932 and EPSRC Grant EP/K034383/1. The third author was supported by ARC Grants DP160100932 and FT160100094.application/pdfen-AU© 2021 American Mathematical Society202110.1090/mcom/36522021-12-19