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

Dirichlet characters