FLINT3.7.0-dev
/

mag_hurwitz_zeta_uiui

Synopsis#include <flint/mag.h>
void mag_hurwitz_zeta_uiui(mag_t res, ulong s, ulong a)source

Sets res to an upper bound for ζ(s,a)=∑k=0∞(k+a)−s\zeta(s, a) = \sum_{k=0}^{\infty} (k+a)^{-s}.

The bound is

ζ(s,a)≤1as+1(s−1)as−1,\zeta(s,a) \le \frac{1}{a^s} + \frac{1}{(s-1) a^{s-1}},

obtained by comparing the sum with an integral. It is +∞+\infty if s≤1s \le 1 or a=0a = 0.

Cite this page

The FLINT team, “mag_hurwitz_zeta_uiui (mag.h),” FLINT: Fast Library for Number Theory, documentation, version 3.7.0-dev, 2026. https://flintlib.org/doc/mag/mag_hurwitz_zeta_uiui.html (generated 2026-11-02).