In his seminal paper, Atle Selberg introduced fundamental new ideas into the
classical theory of automorphic forms, a theory whose origins lie in the works of Riemann, Klein, and Poincare. These ideas are connected with an extension of the earlier notion of an automorphic function (or form). Instead of an analytic automorphic function, Selberg considered a mapping which is automorphic relative to a given finite-dimensional unitary representation of a discrete group and is an eigen-function for a commutative ring of elliptic differential operators.