Fungrim home page

Fungrim entry: d8c6d1

χq . 1 ⁣(n)={1,gcd⁡ ⁣(n,q)=10,otherwise\chi_{q \, . \, 1}\!\left(n\right) = \begin{cases} 1, & \gcd\!\left(n, q\right) = 1\\0, & \text{otherwise}\\ \end{cases}
Assumptions:q∈Z≥1  and⁡  n∈Zq \in \mathbb{Z}_{\ge 1} \;\mathbin{\operatorname{and}}\; n \in \mathbb{Z}
TeX:
\chi_{q \, . \, 1}\!\left(n\right) = \begin{cases} 1, & \gcd\!\left(n, q\right) = 1\\0, & \text{otherwise}\\ \end{cases}

q \in \mathbb{Z}_{\ge 1} \;\mathbin{\operatorname{and}}\; n \in \mathbb{Z}
Definitions:
Fungrim symbol Notation Short description
DirichletCharacterχq . ℓ\chi_{q \, . \, \ell} Dirichlet character
GCDgcd⁡ ⁣(a,b)\gcd\!\left(a, b\right) Greatest common divisor
ZZGreaterEqualZ≥n\mathbb{Z}_{\ge n} Integers greater than or equal to n
ZZZ\mathbb{Z} Integers
Source code for this entry:
Entry(ID("d8c6d1"),
    Formula(Equal(DirichletCharacter(q, 1, n), Cases(Tuple(1, Equal(GCD(n, q), 1)), Tuple(0, Otherwise)))),
    Variables(q, n),
    Assumptions(And(Element(q, ZZGreaterEqual(1)), Element(n, ZZ))))

Topics using this entry

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

2021-03-15 19:12:00.328586 UTC