Automorphic forms of higher order

In this paper a theory of Hecke operators for higher order modular forms is established. The definition of cusp forms and attached L-functions is extended beyond the realm of parabolic invariants. The role of representation theoretic methods is clarified and, motivated by higher order forms, new convolution products of L-functions are introduced.

A new multiple Dirichlet series induced by a higher order form

A multiple Dirichlet series in two variables is constructed as a Mellin transform of a higher order Eisenstein series. It is shown to extend to a meromorphic function and satisfy two independent functional equations.