_acb_poly_powsum_one_series_sieved
Synopsis
#include <flint/acb_poly.h>void _acb_poly_powsum_one_series_sieved(acb_ptr z, const acb_t s, slong n, slong len, slong prec)sourceSets {z, len} to \sum_{k=1}^{n} k^{-(s+t)} as a power series in t. Powers of composite k = ij are computed as products i^{-(s+t)} j^{-(s+t)} of stored powers, and the even terms are grouped as a polynomial in 2^{-(s+t)}. This takes about n / \log n powers, n/2 multiplications and storage for n/6 power series, and is faster than the naive algorithm only when len is small.
Cite this page
The FLINT team, “_acb_poly_powsum_one_series_sieved (acb_poly.h),” FLINT: Fast Library for Number Theory, documentation, version 3.7.0-dev, 2026. https://flintlib.org/doc/acb_poly/_acb_poly_powsum_one_series_sieved.html (generated 2026-10-20).
@misc{flint-doc-acb-poly-acb-poly-powsum-one-series-sieved,
author = {{The FLINT team}},
title = {{\_acb\_poly\_powsum\_one\_series\_sieved (acb\_poly.h)}},
howpublished = {FLINT: Fast Library for Number Theory, documentation, version 3.7.0-dev},
year = {2026},
url = {https://flintlib.org/doc/acb_poly/_acb_poly_powsum_one_series_sieved.html},
note = {Generated 2026-10-20}
}