_acb_poly_zeta_series, acb_poly_zeta_series
#include <flint/acb_poly.h>void _acb_poly_zeta_series(acb_ptr res, acb_srcptr h, slong hlen, const acb_t a, int deflate, slong len, slong prec)sourcevoid acb_poly_zeta_series(acb_poly_t res, const acb_poly_t f, const acb_t a, int deflate, slong n, slong prec)sourceSet res to the Hurwitz zeta function \zeta(s, a) of the power series s = f for a constant a, truncated to length n; a = 1 gives the Riemann zeta function. If deflate is nonzero, \zeta(s, a) + 1/(1 - s) is computed, which is finite at s = 1; with s = 1 + x this gives the Stieltjes constants, \sum_{k=0}^{n-1} \frac{(-1)^k}{k!} \gamma_k(a) x^k.
The series at the constant term is computed by acb_dirichlet_zeta_jet if a = 1 and by _acb_poly_zeta_cpx_series otherwise, and then composed with the nonconstant part of s. acb_dirichlet_zeta_jet uses the functional equation if the real part of the midpoint is negative, the Riemann–Siegel formula for at most two coefficients at very large imaginary parts (above about 60\,\mathit{prec}^{3/2}), and Euler–Maclaurin summation otherwise.
Guides#
The FLINT team, “_acb_poly_zeta_series, acb_poly_zeta_series (acb_poly.h),” FLINT: Fast Library for Number Theory, documentation, version 3.7.0-dev, 2026. https://flintlib.org/doc/acb_poly/_acb_poly_zeta_series.html (generated 2026-10-20).
@misc{flint-doc-acb-poly-acb-poly-zeta-series,
author = {{The FLINT team}},
title = {{\_acb\_poly\_zeta\_series, acb\_poly\_zeta\_series (acb\_poly.h)}},
howpublished = {FLINT: Fast Library for Number Theory, documentation, version 3.7.0-dev},
year = {2026},
url = {https://flintlib.org/doc/acb_poly/_acb_poly_zeta_series.html},
note = {Generated 2026-10-20}
}