`gr_zeta_zero, gr_zeta_zero_vec, gr_zeta_nzeros`

Synopsis#include <flint/gr_special.h>

int gr_zeta_zero(gr_ptr res, const fmpz_t n, gr_ctx_t ctx)source

int gr_zeta_zero_vec(gr_ptr res, const fmpz_t n, slong len, gr_ctx_t ctx)source

int gr_zeta_nzeros(gr_ptr res, gr_srcptr t, gr_ctx_t ctx)source

Set res to the $n$ -th nontrivial zero $\rho_n = 1/2 + i t_n$ of $\zeta(s)$ in the upper half-plane, counted from $n = 1$ by increasing height; to the len consecutive zeros $\rho_n, \rho_{n+1}, \ldots$ ; or to the number $N(t)$ of zeros with imaginary part in $(0, t]$ . The ball implementations return GR_UNABLE for $n < 1$ and for non-real or non-finite $t$ .

Cite this page

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

@misc{flint-doc-gr-special-gr-zeta-zero,
  author       = {{The FLINT team}},
  title        = {{gr\_zeta\_zero, gr\_zeta\_zero\_vec, gr\_zeta\_nzeros (gr\_special.h)}},
  howpublished = {FLINT: Fast Library for Number Theory, documentation, version 3.7.0-dev},
  year         = {2026},
  url          = {https://flintlib.org/doc/gr_special/gr_zeta_zero.html},
  note         = {Generated 2026-11-02}
}

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