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Fungrim entry: 47d430

Gq={χq.:{1,2,,max ⁣(q,2)1}andgcd ⁣(,q)=1}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:qZ1q \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
DirichletGroupGqG_{q} Dirichlet characters with given modulus
DirichletCharacterχq.\chi_{q \, . \, \ell} Dirichlet character
Range{a,a+1,,b}\{a, a + 1, \ldots, b\} Integers between given endpoints
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), 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.

2019-10-05 13:11:19.856591 UTC