FLINT3.7.0-dev
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acb_mzeta_mzv_star, acb_mzeta_mzv_t

Synopsis#include <flint/acb_mzeta.h>
void acb_mzeta_mzv_star(arb_t res, const ulong * s, slong r, slong prec)source
void acb_mzeta_mzv_t(acb_t res, const ulong * s, slong r, const acb_t t, slong prec)source

The multiple zeta star value ζ⋆(s1,…,sr)=∑n1≥⋯≥nr≥1n1−s1⋯nr−sr\zeta^\star(s_1, \ldots, s_r) = \sum_{n_1 \ge \cdots \ge n_r \ge 1} n_1^{-s_1} \cdots n_r^{-s_r}, respectively Yamamoto's interpolation [Yam2013]

ζt(s)=∑pt r−depth⁡(p)ζ(p),\zeta^t(s) = \sum_{p} t^{\,r - \operatorname{depth}(p)} \zeta(p),

the sum over the 2r−12^{r-1} indices pp obtained from ss by replacing some of the commas by plus signs (t=0t = 0 gives ζ(s)\zeta(s), t=1t = 1 gives ζ⋆(s)\zeta^\star(s)), as with PARI/GP's zetamult(s, t). The values ζ(p)\zeta(p) are computed together, sharing their subwords, and the result is a polynomial in tt evaluated at t; for tt far from [0,1][0, 1] the absolute error is relative to the largest term. Depth at most 24.

References#

Cite this page

The FLINT team, “acb_mzeta_mzv_star, acb_mzeta_mzv_t (acb_mzeta.h),” FLINT: Fast Library for Number Theory, documentation, version 3.7.0-dev, 2026. https://flintlib.org/doc/acb_mzeta/acb_mzeta_mzv_star.html (generated 2026-11-07).