In mathematics, an automorphic function is a function on a space that is invariant under the action of some group, in other words a function on the quotient space.

In harmonic analysis and number theory, an automorphic form is a well-behaved function from a topological group G to the complex numbers (or complex vector space) which is invariant under the action of a discrete subgroup of the topological group.

(mathematics) A number whose decimal representation of its square ends in itself.