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Fungrim entry: 47d430

Gq={χq(,):{1,2,max ⁣(q,2)1}andgcd ⁣(,q)=1}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:qZ1q \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
DirichletGroupGqG_{q} Dirichlet characters with given modulus
SetBuilder{f ⁣(x):P ⁣(x)}\left\{ f\!\left(x\right) : P\!\left(x\right) \right\} Set comprehension
DirichletCharacterχq(,)\chi_{q}(\ell, \cdot) Dirichlet character
ZZBetween{a,a+1,b}\{a, a + 1, \ldots b\} Integers between a and b inclusive
GCDgcd ⁣(a,b)\gcd\!\left(a, b\right) Greatest common divisor
ZZGreaterEqualZn\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