# Fungrim entry: 47d430

$G_{q} = \left\{ \chi_{q \, . \, \ell} : \ell \in \{1, 2, \ldots, \max\!\left(q, 2\right) - 1\} \;\mathbin{\operatorname{and}}\; \gcd\!\left(\ell, q\right) = 1 \right\}$
Assumptions:$q \in \mathbb{Z}_{\ge 1}$
TeX:
G_{q} = \left\{ \chi_{q \, . \, \ell} : \ell \in \{1, 2, \ldots, \max\!\left(q, 2\right) - 1\} \;\mathbin{\operatorname{and}}\; \gcd\!\left(\ell, q\right) = 1 \right\}

q \in \mathbb{Z}_{\ge 1}
Definitions:
Fungrim symbol Notation Short description
DirichletGroup$G_{q}$ Dirichlet characters with given modulus
DirichletCharacter$\chi_{q \, . \, \ell}$ Dirichlet character
Range$\{a, a + 1, \ldots, b\}$ Integers between given endpoints
GCD$\gcd\!\left(a, b\right)$ Greatest common divisor
ZZGreaterEqual$\mathbb{Z}_{\ge n}$ Integers greater than or equal to n
Source code for this entry:
Entry(ID("47d430"),
Formula(Equal(DirichletGroup(q), Set(DirichletCharacter(q, ell), For(ell), And(Element(ell, Range(1, Sub(Max(q, 2), 1))), Equal(GCD(ell, q), 1))))),
Variables(q),
Assumptions(Element(q, ZZGreaterEqual(1))))

## Topics using this entry

Copyright (C) Fredrik Johansson and contributors. Fungrim is provided under the MIT license. The source code is on GitHub.

2020-04-08 16:14:44.404316 UTC