# Fungrim entry: 1b2d8a

$\mathop{\operatorname{zeros}\,}\limits_{\tau \in \mathbb{H}} j(\tau) = \left\{ \gamma \circ {e}^{2 \pi i / 3} : \gamma \in \operatorname{PSL}_2(\mathbb{Z}) \right\}$
TeX:
\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\}
Definitions:
Fungrim symbol Notation Short description
Zeros$\mathop{\operatorname{zeros}\,}\limits_{x \in S} f(x)$ Zeros (roots) of function
ModularJ$j(\tau)$ Modular j-invariant
HH$\mathbb{H}$ Upper complex half-plane
ModularGroupAction$\gamma \circ \tau$ Action of modular group
Exp${e}^{z}$ Exponential function
Pi$\pi$ The constant pi (3.14...)
ConstI$i$ Imaginary unit
PSL2Z$\operatorname{PSL}_2(\mathbb{Z})$ Modular group (canonical representatives)
Source code for this entry:
Entry(ID("1b2d8a"),
Formula(Equal(Zeros(ModularJ(tau), ForElement(tau, HH)), Set(ModularGroupAction(gamma, Exp(Div(Mul(Mul(2, Pi), ConstI), 3))), ForElement(gamma, PSL2Z)))))

## Topics using this entry

Copyright (C) Fredrik Johansson and contributors. Fungrim is provided under the MIT license. The source code is on GitHub.

2021-03-15 19:12:00.328586 UTC