`acb_dirichlet_powsum_sieved`

Synopsis#include <flint/acb_dirichlet.h>

void acb_dirichlet_powsum_sieved(acb_ptr z, const acb_t s, ulong n, slong len, slong prec)source

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 2026-11-02).

@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 2026-11-02}
}

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