gr_dirichlet_hardy_theta, gr_dirichlet_hardy_z
Synopsis
#include <flint/gr_special.h>int gr_dirichlet_hardy_theta(gr_ptr res, const dirichlet_group_t G, const dirichlet_char_t chi, gr_srcptr t, gr_ctx_t ctx)sourceint gr_dirichlet_hardy_z(gr_ptr res, const dirichlet_group_t G, const dirichlet_char_t chi, gr_srcptr t, gr_ctx_t ctx)sourceSet res to the Hardy theta function \theta(t) and Hardy Z-function Z(t) of the character chi, defined so that Z(t) = e^{i \theta(t)} L(1/2 + it, \chi) is real for real t, with the same rings as gr_dirichlet_l.
Cite this page
The FLINT team, “gr_dirichlet_hardy_theta, gr_dirichlet_hardy_z (gr_special.h),” FLINT: Fast Library for Number Theory, documentation, version 3.7.0-dev, 2026. https://flintlib.org/doc/gr_special/gr_dirichlet_hardy_theta.html (generated 2026-10-20).
@misc{flint-doc-gr-special-gr-dirichlet-hardy-theta,
author = {{The FLINT team}},
title = {{gr\_dirichlet\_hardy\_theta, gr\_dirichlet\_hardy\_z (gr\_special.h)}},
howpublished = {FLINT: Fast Library for Number Theory, documentation, version 3.7.0-dev},
year = {2026},
url = {https://flintlib.org/doc/gr_special/gr_dirichlet_hardy_theta.html},
note = {Generated 2026-10-20}
}