Analogues elliptiques des nombres multiz\'etas

TL;DR

This paper explores elliptic functions defined through iterated integrals, linking them to elliptic associators and Lie algebra structures, thereby advancing the understanding of elliptic special functions.

Contribution

It introduces a new class of elliptic functions as iterated integrals and connects them to elliptic associators via Lie algebra representations, extending previous theoretical frameworks.

Findings

Established a relation between elliptic iterated integrals and elliptic associators.

Provided a functional realization of Lie algebras related to elliptic functions.

Enhanced the theoretical understanding of elliptic special functions.

Abstract

We study functions of an elliptic parameter, which are defined as iterated integrals of elliptic functions. We establish their relation with the "elliptic associators" of our previous work, by means of a functional realization of Lie algebras appearing in that work.