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Fungrim entry: 1b2d8a

zerosτHj(τ)={γe2πi/3:γPSL2(Z)}\mathop{\operatorname{zeros}\,}\limits_{\tau \in \mathbb{H}} j(\tau) = \left\{ \gamma \circ {e}^{2 \pi i / 3} : \gamma \in \operatorname{PSL}_2(\mathbb{Z}) \right\}
\mathop{\operatorname{zeros}\,}\limits_{\tau \in \mathbb{H}} j(\tau) = \left\{ \gamma \circ {e}^{2 \pi i / 3} : \gamma \in \operatorname{PSL}_2(\mathbb{Z}) \right\}
Fungrim symbol Notation Short description
ZeroszerosxSf(x)\mathop{\operatorname{zeros}\,}\limits_{x \in S} f(x) Zeros (roots) of function
ModularJj(τ)j(\tau) Modular j-invariant
HHH\mathbb{H} Upper complex half-plane
ModularGroupActionγτ\gamma \circ \tau Action of modular group
Expez{e}^{z} Exponential function
Piπ\pi The constant pi (3.14...)
ConstIii Imaginary unit
PSL2ZPSL2(Z)\operatorname{PSL}_2(\mathbb{Z}) Modular group (canonical representatives)
Source code for this entry:
    Formula(Equal(Zeros(ModularJ(tau), ForElement(tau, HH)), Set(ModularGroupAction(gamma, Exp(Div(Mul(Mul(2, Pi), ConstI), 3))), ForElement(gamma, PSL2Z)))))

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2021-03-15 19:12:00.328586 UTC