Iterated integrals and unipotent periods on families of marked elliptic curves

TL;DR

This paper explores the relationship between iterated integrals, unipotent periods, and special values like multiple zeta values on families of elliptic curves, advancing understanding of their mathematical structure.

Contribution

It introduces a new framework connecting iterated integrals and unipotent periods on elliptic curves with multiple zeta values and elliptic multiple zeta values.

Findings

Expressed iterated integrals as unipotent periods on elliptic curves.

Linked unipotent periods to multiple zeta values.

Provided a new perspective on the structure of elliptic periods.

Abstract

We describe iterated integrals as unipotent periods on families of marked elliptic curves in terms of multiple zeta values and elliptic multiple zeta values.