Duality/Sum formulas for iterated integrals and their application to multiple zeta values

TL;DR

This paper explores linear relations among iterated integrals on the Riemann sphere, extending duality and sum formulas for multiple zeta values, revealing new algebraic structures and relations.

Contribution

It generalizes duality and sum formulas for multiple zeta values to a broader class of iterated integrals on the Riemann sphere.

Findings

Generalized duality formula for iterated integrals

Extended sum formula for multiple zeta values

Identified new linear relations among iterated integrals

Abstract

We investigate linear relations among a class of iterated integrals on the Riemann sphere minus four points $0,1,z$ and $\infty$. Generalization of the duality formula and the sum formula for multiple zeta values to the iterated integrals are given.