acb_dirichlet_qseries_arb_powers_naive, acb_dirichlet_qseries_arb_powers_smallorder
Synopsis
#include <flint/acb_dirichlet.h>void acb_dirichlet_qseries_arb_powers_naive(acb_t res, const arb_t x, int parity, const ulong * a, const acb_dirichlet_roots_t z, slong len, slong prec)sourcevoid acb_dirichlet_qseries_arb_powers_smallorder(acb_t res, const arb_t x, int parity, const ulong * a, const acb_dirichlet_roots_t z, slong len, slong prec)sourceSet res to \sum_{n<\text{len}} n^p z^{a_n} x^{n^2}, where p is parity (0 or 1), z is the root of unity of z, and the exponents a_n are given (with a special value for \chi(n) = 0, as produced by dirichlet_chi_vec_order). The naive version sums the series as written; the smallorder version sums it in the quotient ring by the cyclotomic polynomial and evaluates at the root of unity only at the end, ignoring z except for its order.
Cite this page
The FLINT team, “acb_dirichlet_qseries_arb_powers_naive, acb_dirichlet_qseries_arb_powers_smallorder (acb_dirichlet.h),” FLINT: Fast Library for Number Theory, documentation, version 3.7.0-dev, 2026. https://flintlib.org/doc/acb_dirichlet/acb_dirichlet_qseries_arb_powers_naive.html (generated 2026-10-20).
@misc{flint-doc-acb-dirichlet-acb-dirichlet-qseries-arb-powers-naive,
author = {{The FLINT team}},
title = {{acb\_dirichlet\_qseries\_arb\_powers\_naive, acb\_dirichlet\_qseries\_arb\_powers\_smallorder (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_qseries_arb_powers_naive.html},
note = {Generated 2026-10-20}
}