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Fungrim entry: 89e79d

(εj ⁣(a,b,c,d))8=1{\left(\varepsilon_{j}\!\left(a, b, c, d\right)\right)}^{8} = 1
Assumptions:j{1,2,3,4}and(abcd)SL2(Z)j \in \left\{1, 2, 3, 4\right\} \,\mathbin{\operatorname{and}}\, \begin{pmatrix} a & b \\ c & d \end{pmatrix} \in \operatorname{SL}_2(\mathbb{Z})
TeX:
{\left(\varepsilon_{j}\!\left(a, b, c, d\right)\right)}^{8} = 1

j \in \left\{1, 2, 3, 4\right\} \,\mathbin{\operatorname{and}}\, \begin{pmatrix} a & b \\ c & d \end{pmatrix} \in \operatorname{SL}_2(\mathbb{Z})
Definitions:
Fungrim symbol Notation Short description
Powab{a}^{b} Power
JacobiThetaEpsilonεj ⁣(a,b,c,d)\varepsilon_{j}\!\left(a, b, c, d\right) Root of unity in modular transformation of Jacobi theta functions
Matrix2x2(abcd)\begin{pmatrix} a & b \\ c & d \end{pmatrix} Two by two matrix
SL2ZSL2(Z)\operatorname{SL}_2(\mathbb{Z}) Modular group
Source code for this entry:
Entry(ID("89e79d"),
    Formula(Equal(Pow(JacobiThetaEpsilon(j, a, b, c, d), 8), 1)),
    Variables(j, a, b, c, d),
    Assumptions(And(Element(j, Set(1, 2, 3, 4)), Element(Matrix2x2(a, b, c, d), SL2Z))))

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2019-11-19 15:10:20.037976 UTC