# Fungrim entry: 47d430

$G_{q} = \left\{ \chi_{q}(\ell, \cdot) : \ell \in \{1, 2, \ldots \max\!\left(q, 2\right) - 1\} \,\mathbin{\operatorname{and}}\, \gcd\!\left(\ell, q\right) = 1 \right\}$
Assumptions:$q \in \mathbb{Z}_{\ge 1}$
TeX:
G_{q} = \left\{ \chi_{q}(\ell, \cdot) : \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
SetBuilder$\left\{ f\!\left(x\right) : P\!\left(x\right) \right\}$ Set comprehension
DirichletCharacter$\chi_{q}(\ell, \cdot)$ Dirichlet character
ZZBetween$\{a, a + 1, \ldots b\}$ Integers between a and b inclusive
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), SetBuilder(DirichletCharacter(q, ell), ell, And(Element(ell, ZZBetween(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.

2019-08-17 11:32:46.829430 UTC