Fungrim symbol: ModularGroupAction

Symbol: ModularGroupAction —

\gamma \circ \tau

— Action of modular group

Domain	Codomain
$\gamma \in \operatorname{SL}_2(\mathbb{Z}) \;\mathbin{\operatorname{and}}\; \tau \in \mathbb{H}$	$\gamma \circ \tau \in \mathbb{H}$

Table data:

\left(P, Q\right)

such that

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

Definitions:

Fungrim symbol	Notation	Short description
`ModularGroupAction`	$\gamma \circ \tau$	Action of modular group
`SL2Z`	$\operatorname{SL}_2(\mathbb{Z})$	Modular group
`HH`	$\mathbb{H}$	Upper complex half-plane

Source code for this entry:

Entry(ID("76de9d"),
    SymbolDefinition(ModularGroupAction, ModularGroupAction(gamma, tau), "Action of modular group"),
    Table(TableRelation(Tuple(P, Q), Implies(P, Q)), TableHeadings(Description("Domain"), Description("Codomain")), List(Tuple(And(Element(gamma, SL2Z), Element(tau, HH)), Element(ModularGroupAction(gamma, tau), HH)))))

Topics using this symbol

The symbol ModularGroupAction appears in 4 topics:

Modular transformations (in 4 entries)
Modular lambda function (in 1 entries)
Modular j-invariant (in 1 entries)
Eisenstein series (in 1 entries)

Entries using this symbol

The symbol ModularGroupAction appears in 7 entries: