Automorphic forms of higher order

TL;DR

This paper develops a new theory of Hecke operators for higher order modular forms, extending classical concepts like cusp forms and L-functions, and introduces novel convolution products inspired by representation theory.

Contribution

It establishes a framework for higher order Hecke operators, extends cusp form and L-function definitions, and introduces new convolution products based on representation theoretic methods.

Findings

Defined Hecke operators for higher order forms

Extended cusp forms and L-functions beyond parabolic invariants

Introduced new convolution products of L-functions

Abstract

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.