acb_dirichlet_powsum_sieved
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. Powers of composite k = ij are computed as i^{-s} j^{-s} from a table, and the even terms are grouped as a polynomial in 2^{-(s+x)}. This needs about n / \log n powers, n/2 multiplications and storage for n/6 power series, so it is only faster than the naive sum for small len.
Cite this page
The FLINT team, “acb_dirichlet_powsum_sieved (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_sieved.html (generated 2026-10-20).
@misc{flint-doc-acb-dirichlet-acb-dirichlet-powsum-sieved,
author = {{The FLINT team}},
title = {{acb\_dirichlet\_powsum\_sieved (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_sieved.html},
note = {Generated 2026-10-20}
}