Automorphic forms of higher order

Anton Deitmar, Nikolaos Diamantis

Published 2008-02-04, updated 2008-10-12Version 3

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.