acb_dirichlet_zeta
Synopsis
#include <flint/acb_dirichlet.h>Sets res to \zeta(s), choosing the algorithm from s and prec: exact values at integers (Bernoulli numbers for negative integers, arb_zeta_ui for positive ones), the Riemann–Siegel formula for |\operatorname{Im}(s)| \ge 24 \, p^{3/2} and |\operatorname{Re}(s)| \le 10 + p/10 at precision p, and Euler–Maclaurin summation otherwise, after the reflection formula for \operatorname{Re}(s) < 0. The result is indeterminate if s contains the pole s = 1.
Cite this page
The FLINT team, “acb_dirichlet_zeta (acb_dirichlet.h),” FLINT: Fast Library for Number Theory, documentation, version 3.7.0-dev, 2026. https://flintlib.org/doc/acb_dirichlet/acb_dirichlet_zeta.html (generated 2026-10-20).
@misc{flint-doc-acb-dirichlet-acb-dirichlet-zeta,
author = {{The FLINT team}},
title = {{acb\_dirichlet\_zeta (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_zeta.html},
note = {Generated 2026-10-20}
}