acb_dirichlet_hardy_z
Synopsis
#include <flint/acb_dirichlet.h>void acb_dirichlet_hardy_z(acb_ptr res, const acb_t t, const dirichlet_group_t G, const dirichlet_char_t chi, slong len, slong prec)sourceSets res to the first len Taylor coefficients of Z(t), computed as e^{i\theta(t)} L(1/2 + it, \chi) with acb_dirichlet_l_jet. For the Riemann zeta function, this uses the Riemann–Siegel formula when t is large and len \le 2. If t is real, the imaginary parts are set to exactly zero.
Cite this page
The FLINT team, “acb_dirichlet_hardy_z (acb_dirichlet.h),” FLINT: Fast Library for Number Theory, documentation, version 3.7.0-dev, 2026. https://flintlib.org/doc/acb_dirichlet/acb_dirichlet_hardy_z.html (generated 2026-10-20).
@misc{flint-doc-acb-dirichlet-acb-dirichlet-hardy-z,
author = {{The FLINT team}},
title = {{acb\_dirichlet\_hardy\_z (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_hardy_z.html},
note = {Generated 2026-10-20}
}