Automorphic function

This term is related to: action on complex manifolds
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Definition

Let $G$ be a group acting on a complex manifold $X$. An automorphic function for this action is a map $f$ from $G$ to the space of holomorphic functions from $G$ to $\mathbb{C}$ satisfying any of the following equivalent conditions:

• There exists a function $\gamma :G\times X\to {\mathbb{C}}^{*}$ such that: