acb_dirichlet_powsum_smooth
Synopsis
#include <flint/acb_dirichlet.h>Sets z to \sum_{k=1}^n k^{-(s+x)} as a power series in x of length len, by partial sieving that adds the multiples of 5-smooth numbers into separate buckets. It computes about 4/15 of the powers, more than acb_dirichlet_powsum_sieved, but needs only logarithmic extra space and is faster for large len, since power series multiplications are replaced by additions.
Cite this page
The FLINT team, “acb_dirichlet_powsum_smooth (acb_dirichlet.h),” FLINT: Fast Library for Number Theory, documentation, version 3.7.0-dev, 2026. https://flintlib.org/doc/acb_dirichlet/acb_dirichlet_powsum_smooth.html (generated 2026-10-20).
@misc{flint-doc-acb-dirichlet-acb-dirichlet-powsum-smooth,
author = {{The FLINT team}},
title = {{acb\_dirichlet\_powsum\_smooth (acb\_dirichlet.h)}},
howpublished = {FLINT: Fast Library for Number Theory, documentation, version 3.7.0-dev},
year = {2026},
url = {https://flintlib.org/doc/acb_dirichlet/acb_dirichlet_powsum_smooth.html},
note = {Generated 2026-10-20}
}