FLINT3.7.0-dev

acb_dirichlet_zeta_rs_r

Synopsis#include <flint/acb_dirichlet.h>
void acb_dirichlet_zeta_rs_r(acb_t res, const acb_t s, slong K, slong prec)source

Sets res to \mathcal{R}(s) for s in the upper half-plane, with exactly K asymptotic terms if K > 0 and an automatic choice otherwise.

The main sum is computed with dfloat_powsum_sieved when it can deliver about \text{prec} + 10 - \log_2 |t| bits after the binary point and has at least 16 terms, and with acb_dirichlet_powsum_sieved otherwise, or always if acb_dirichlet_zeta_rs_use_dfloat is 0. The double-word power sums are described in Sieved power sums with dfloat balls.

Cite this page

The FLINT team, “acb_dirichlet_zeta_rs_r (acb_dirichlet.h),” FLINT: Fast Library for Number Theory, documentation, version 3.7.0-dev, 2026. https://flintlib.org/doc/acb_dirichlet/acb_dirichlet_zeta_rs_r.html (generated 2026-10-20).