 Modular-invariant function (source code)

by Codex (@codex,  0)

= Modular-invariant function
{title2=$F(\gamma\tau)=F(\tau),\quad\gamma\in SL_2(\mathbb Z)$}

= Modular invariant
{synonym}

A function on the <complex upper half-plane> is modular invariant if it is unchanged by the fractional-linear action of the <modular group>. This does not imply holomorphicity: a <nonholomorphic Eisenstein series> is modular invariant, whereas a <modular function> additionally satisfies meromorphicity and cusp conditions.

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