Fungrim entry: 441301

\left|\mathop{\operatorname{solutions}\,}\limits_{\tau \in \mathcal{F}} \left[j\!\left(\tau\right) = z\right]\right| = 1

Assumptions:

z \in \mathbb{C}

TeX:

\left|\mathop{\operatorname{solutions}\,}\limits_{\tau \in \mathcal{F}} \left[j\!\left(\tau\right) = z\right]\right| = 1

z \in \mathbb{C}

Definitions:

Fungrim symbol	Notation	Short description
`Cardinality`	$\left\|S\right\|$	Set cardinality
`ModularJ`	$j\!\left(\tau\right)$	Modular j-invariant
`ModularGroupFundamentalDomain`	$\mathcal{F}$	Fundamental domain for action of the modular group
`CC`	$\mathbb{C}$	Complex numbers

Source code for this entry:

Entry(ID("441301"),
    Formula(Equal(Cardinality(Solutions(Brackets(Equal(ModularJ(tau), z)), tau, Element(tau, ModularGroupFundamentalDomain))), 1)),
    Variables(z),
    Assumptions(Element(z, CC)))

Topics using this entry

Modular j-invariant

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

2019-06-18 07:49:59.356594 UTC