`acb_dirichlet_zeta_bound`

Synopsis#include <flint/acb_dirichlet.h>

void acb_dirichlet_zeta_bound(mag_t res, const acb_t s)source

Sets res to an upper bound for |\zeta(s)|, computed quickly: in and slightly around the critical strip by formula (43.3) of [Rad1973], to the right by the value at \operatorname{Re}(s), and to the left by the functional equation.

References#

[Rad1973] H. Rademacher, Topics in analytic number theory, Springer, 1973.

Cite this page

The FLINT team, “acb_dirichlet_zeta_bound (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_bound.html (generated 2026-10-20).

@misc{flint-doc-acb-dirichlet-acb-dirichlet-zeta-bound,
  author       = {{The FLINT team}},
  title        = {{acb\_dirichlet\_zeta\_bound (acb\_dirichlet.h)}},
  howpublished = {FLINT: Fast Library for Number Theory, documentation, version 3.7.0-dev},
  year         = {2026},
  url          = {https://flintlib.org/doc/acb_dirichlet/acb_dirichlet_zeta_bound.html},
  note         = {Generated 2026-10-20}
}

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