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Fungrim entry: d9a187

χ ⁣(n)=χq(,n)   where χ=χq(,)\chi\!\left(n\right) = \chi_{q}(\ell, n)\; \text{ where } \chi = \chi_{q}(\ell, \cdot)
This is simply a syntactical definition of character evaluation.
Assumptions:qZ1and{1,2,max ⁣(q,2)1}andgcd ⁣(,q)=1andnZq \in \mathbb{Z}_{\ge 1} \,\mathbin{\operatorname{and}}\, \ell \in \{1, 2, \ldots \max\!\left(q, 2\right) - 1\} \,\mathbin{\operatorname{and}}\, \gcd\!\left(\ell, q\right) = 1 \,\mathbin{\operatorname{and}}\, n \in \mathbb{Z}
\chi\!\left(n\right) = \chi_{q}(\ell, n)\; \text{ where } \chi = \chi_{q}(\ell, \cdot)

q \in \mathbb{Z}_{\ge 1} \,\mathbin{\operatorname{and}}\, \ell \in \{1, 2, \ldots \max\!\left(q, 2\right) - 1\} \,\mathbin{\operatorname{and}}\, \gcd\!\left(\ell, q\right) = 1 \,\mathbin{\operatorname{and}}\, n \in \mathbb{Z}
Fungrim symbol Notation Short description
DirichletCharacterχq(,)\chi_{q}(\ell, \cdot) Dirichlet character
ZZGreaterEqualZn\mathbb{Z}_{\ge n} Integers greater than or equal to n
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
ZZZ\mathbb{Z} Integers
Source code for this entry:
    Formula(Where(Equal(chi(n), DirichletCharacter(q, ell, n)), Equal(chi, DirichletCharacter(q, ell)))),
    Description("This is simply a syntactical definition of character evaluation."),
    Variables(q, ell, n),
    Assumptions(And(Element(q, ZZGreaterEqual(1)), Element(ell, ZZBetween(1, Sub(Max(q, 2), 1))), Equal(GCD(ell, q), 1), Element(n, ZZ))))

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2019-08-19 14:38:23.809000 UTC