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Fungrim entry: fc4f6a

χ4(3,n)={1,n1(mod4)1,n3(mod4)0,otherwise\chi_{4}(3, n) = \begin{cases} 1, & n \equiv 1 \pmod {4}\\-1, & n \equiv 3 \pmod {4}\\0, & \text{otherwise}\\ \end{cases}
Assumptions:nZn \in \mathbb{Z}
TeX:
\chi_{4}(3, n) = \begin{cases} 1, & n \equiv 1 \pmod {4}\\-1, & n \equiv 3 \pmod {4}\\0, & \text{otherwise}\\ \end{cases}

n \in \mathbb{Z}
Definitions:
Fungrim symbol Notation Short description
DirichletCharacterχq(,)\chi_{q}(\ell, \cdot) Dirichlet character
ZZZ\mathbb{Z} Integers
Source code for this entry:
Entry(ID("fc4f6a"),
    Formula(Equal(DirichletCharacter(4, 3, n), Cases(Tuple(1, CongruentMod(n, 1, 4)), Tuple(-1, CongruentMod(n, 3, 4)), Tuple(0, Otherwise)))),
    Variables(n),
    Assumptions(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.

2019-09-15 11:00:55.020619 UTC