Iterated Integrals and higher order automorphic forms

TL;DR

This paper explores the relationship between higher order automorphic forms and Chen's iterated integrals, establishing a structure theorem and defining a mixed Hodge structure analogue to advance understanding in number theory and physics.

Contribution

It introduces a novel connection between higher order automorphic forms and Chen's iterated integrals, providing a new structural framework and Hodge theory analogue.

Findings

Proves a structure theorem for automorphic forms of all orders

Defines an analogue of a mixed Hodge structure on higher order automorphic forms

Establishes a link between automorphic forms and Chen's iterated integrals

Abstract

Higher order automorphic forms have recently been introduced to study important questions in number theory and mathematical physics. We investigate the connection between these functions and Chen's iterated integrals. Then using Chen's theory, we prove a structure theorem for automorphic forms of all orders. This allows us to define an analogue of a mixed Hodge structure on a space of higher order automorphic forms.