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Fungrim entry: ea56d1

λ ⁣(ai+bci+d)∈{−1,12,2}\lambda\!\left(\frac{a i + b}{c i + d}\right) \in \left\{-1, \frac{1}{2}, 2\right\}
Assumptions:(abcd)∈SL⁡2(Z)\begin{pmatrix} a & b \\ c & d \end{pmatrix} \in \operatorname{SL}_2(\mathbb{Z})
TeX:
\lambda\!\left(\frac{a i + b}{c i + d}\right) \in \left\{-1, \frac{1}{2}, 2\right\}

\begin{pmatrix} a & b \\ c & d \end{pmatrix} \in \operatorname{SL}_2(\mathbb{Z})
Definitions:
Fungrim symbol Notation Short description
ModularLambdaλ(τ)\lambda(\tau) Modular lambda function
ConstIii Imaginary unit
Matrix2x2(abcd)\begin{pmatrix} a & b \\ c & d \end{pmatrix} Two by two matrix
SL2ZSL⁡2(Z)\operatorname{SL}_2(\mathbb{Z}) Modular group
Source code for this entry:
Entry(ID("ea56d1"),
    Formula(Element(ModularLambda(Div(Add(Mul(a, ConstI), b), Add(Mul(c, ConstI), d))), Set(-1, Div(1, 2), 2))),
    Variables(a, b, c, d),
    Assumptions(Element(Matrix2x2(a, b, c, d), SL2Z)))

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2021-03-15 19:12:00.328586 UTC