`acb_dirichlet_powsum_term`

Synopsis#include <flint/acb_dirichlet.h>

void acb_dirichlet_powsum_term(acb_ptr res, arb_t log_prev, ulong * prev, const acb_t s, ulong k, int integer, int critical_line, slong len, slong prec)

source

Sets res to $k^{-(s+x)}$ as a power series in $x$ of length len. The flags integer and critical_line select optimisations for integer $s$ and for $\operatorname{Re}(s) = 1/2$ .

On input, log_prev holds $\log(\text{prev})$ for the integer *prev; if *prev is close to $k$ , $\log k$ is computed from it. When $\log k$ is computed, log_prev and *prev are overwritten with $\log k$ and $k$ , so that consecutive calls in a power sum reuse it.

Cite this page

The FLINT team, “acb_dirichlet_powsum_term (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_term.html (generated 2026-11-02).

@misc{flint-doc-acb-dirichlet-acb-dirichlet-powsum-term,
  author       = {{The FLINT team}},
  title        = {{acb\_dirichlet\_powsum\_term (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_term.html},
  note         = {Generated 2026-11-02}
}

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