acb_dirichlet_theta_arb, acb_dirichlet_ui_theta_arb
#include <flint/acb_dirichlet.h>void acb_dirichlet_theta_arb(acb_t res, const dirichlet_group_t G, const dirichlet_char_t chi, const arb_t t, slong prec)sourcevoid acb_dirichlet_ui_theta_arb(acb_t res, const dirichlet_group_t G, ulong a, const arb_t t, slong prec)sourceSet res to \Theta_q(\chi, t) for real t > 0; the ui version takes the Conrey number a. The series converges quickly only for t not too small; for t < 1 the caller should use the functional equation above, which is not applied automatically (to avoid recomputing the Gauss sum).
The number of terms is acb_dirichlet_theta_length. For characters of order less than 30 the series is evaluated with acb_dirichlet_qseries_arb_powers_smallorder, otherwise with acb_dirichlet_qseries_arb_powers_naive, and the tail bound of mag_tail_kexpk2_arb is added.
The FLINT team, “acb_dirichlet_theta_arb, acb_dirichlet_ui_theta_arb (acb_dirichlet.h),” FLINT: Fast Library for Number Theory, documentation, version 3.7.0-dev, 2026. https://flintlib.org/doc/acb_dirichlet/acb_dirichlet_theta_arb.html (generated 2026-10-20).
@misc{flint-doc-acb-dirichlet-acb-dirichlet-theta-arb,
author = {{The FLINT team}},
title = {{acb\_dirichlet\_theta\_arb, acb\_dirichlet\_ui\_theta\_arb (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_theta_arb.html},
note = {Generated 2026-10-20}
}