abstract:In mathematics, the general notion of automorphic form is the extension to analytic functions, perhaps of several complex variables, of the theory of modular forms. It is in terms of a Lie group G, to generalise the groups SL(2, R) or PSL(2, R) of modular forms, and a discrete group \Gamma \subset G, to generalise the modular group, or one of its congruence subgroups.