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Fungrim entry: d8c6d1

χq(1,n)={1,gcd ⁣(n,q)=10,otherwise\chi_{q}(1, n) = \begin{cases} 1, & \gcd\!\left(n, q\right) = 1\\0, & \text{otherwise}\\ \end{cases}
Assumptions:qZ1andnZq \in \mathbb{Z}_{\ge 1} \,\mathbin{\operatorname{and}}\, n \in \mathbb{Z}
TeX:
\chi_{q}(1, n) = \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(,)\chi_{q}(\ell, \cdot) Dirichlet character
GCDgcd ⁣(a,b)\gcd\!\left(a, b\right) Greatest common divisor
ZZGreaterEqualZn\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))))

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

2019-08-21 11:44:15.926409 UTC