`dirichlet_group_num_primitive`

Synopsis#include <flint/dirichlet.h>

ulong dirichlet_group_num_primitive(const dirichlet_group_t G)source

Returns the number of primitive characters modulo $q$ : 0 if $q \equiv 2 \pmod 4$ , and otherwise the product over the components of $p - 2$ for $p^1 \| q$ ( $p$ odd), $(p-1)^2 p^{e-2}$ for $p^e \| q$ ( $e \ge 2$ ), 1 for $4 \| q$ and $2^{e-2}$ for $2^e \| q$ , $e \ge 3$ .

Guides#

Characters in the Conrey numbering

Cite this page

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

@misc{flint-doc-dirichlet-dirichlet-group-num-primitive,
  author       = {{The FLINT team}},
  title        = {{dirichlet\_group\_num\_primitive (dirichlet.h)}},
  howpublished = {FLINT: Fast Library for Number Theory, documentation, version 3.7.0-dev},
  year         = {2026},
  url          = {https://flintlib.org/doc/dirichlet/dirichlet_group_num_primitive.html},
  note         = {Generated 2026-11-02}
}

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