Fungrim symbol: ModularJ

Symbol: ModularJ —

j(\tau)

— Modular j-invariant

The modular j-invariant

j(\tau)

is a function of one variable

\tau

in the upper half-plane.

Domain	Codomain
$\tau \in \mathbb{H}$	$j(\tau) \in \mathbb{C}$

Table data:

\left(P, Q\right)

such that

\left(P\right) \;\implies\; \left(Q\right)

Definitions:

Fungrim symbol	Notation	Short description
`ModularJ`	$j(\tau)$	Modular j-invariant
`HH`	$\mathbb{H}$	Upper complex half-plane
`CC`	$\mathbb{C}$	Complex numbers

Source code for this entry:

Entry(ID("70eb98"),
    SymbolDefinition(ModularJ, ModularJ(tau), "Modular j-invariant"),
    Description("The modular j-invariant", ModularJ(tau), "is a function of one variable", tau, "in the upper half-plane."),
    Table(TableRelation(Tuple(P, Q), Implies(P, Q)), TableHeadings(Description("Domain"), Description("Codomain")), List(Tuple(Element(tau, HH), Element(ModularJ(tau), CC)))))

Topics using this symbol

The symbol ModularJ appears in 4 topics:

Modular j-invariant (in 28 entries)
Modular lambda function (in 1 entries)
Jacobi theta functions (in 1 entries)
Eisenstein series (in 1 entries)

Entries using this symbol

The symbol ModularJ appears in 30 entries: