acb_dirichlet_hurwitz_precomp_init
#include <flint/acb_dirichlet.h>void acb_dirichlet_hurwitz_precomp_init(acb_dirichlet_hurwitz_precomp_t pre, const acb_t s, int deflate, slong A, slong K, slong N, slong prec)sourcePrecomputes a grid of N Taylor polynomials of length K for \zeta(s, a + A), for fast evaluation of \zeta(s, a) at a \in (0,1] with fixed s. This costs NK Hurwitz zeta values; each later evaluation costs 2K arithmetic operations plus A powers, with a truncation error O(1/(2AN)^K). With deflate nonzero, the deflated function (without the pole at s = 1) is used.
With A = 0, no precomputation is done and evaluation is the same as calling acb_dirichlet_hurwitz. Otherwise A, K and N must be positive (an exception is thrown otherwise), and the error bound is finite only if K + \operatorname{Re}(s) > 1. To avoid an initial bump that loses precision and slows convergence, AN should be at least about as large as |s|, for instance AN > 0.5 |s|. The error bound is that of Taylor expansion in the parameter.
The FLINT team, “acb_dirichlet_hurwitz_precomp_init (acb_dirichlet.h),” FLINT: Fast Library for Number Theory, documentation, version 3.7.0-dev, 2026. https://flintlib.org/doc/acb_dirichlet/acb_dirichlet_hurwitz_precomp_init.html (generated 2026-10-20).
@misc{flint-doc-acb-dirichlet-acb-dirichlet-hurwitz-precomp-init,
author = {{The FLINT team}},
title = {{acb\_dirichlet\_hurwitz\_precomp\_init (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_hurwitz_precomp_init.html},
note = {Generated 2026-10-20}
}