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# Fungrim entry: d9a187

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

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}
Definitions:
Fungrim symbol Notation Short description
DirichletCharacter$\chi_{q \, . \, \ell}$ Dirichlet character
ZZGreaterEqual$\mathbb{Z}_{\ge n}$ Integers greater than or equal to n
Range$\{a, a + 1, \ldots, b\}$ Integers between given endpoints
GCD$\gcd\!\left(a, b\right)$ Greatest common divisor
ZZ$\mathbb{Z}$ Integers
Source code for this entry:
Entry(ID("d9a187"),
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, Range(1, Sub(Max(q, 2), 1))), Equal(GCD(ell, q), 1), Element(n, ZZ))))

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2021-03-15 19:12:00.328586 UTC