Coproduct Formula for Motivic Version of Yamamoto's Integral

TL;DR

This paper extends Goncharov's coproduct formula to the motivic version of Yamamoto's integral, enabling new computations of motivic multiple zeta values and their coproduct structures.

Contribution

It generalizes Goncharov's coproduct formula to the motivic Yamamoto integral, providing a new framework for analyzing motivic multiple zeta values.

Findings

Derived the coproduct formula for motivic Yamamoto's integral.

Computed coproducts of specific Schur multiple zeta values.

Extended the algebraic understanding of motivic multiple zeta values.

Abstract

Goncharov proved an explicit formula for the coproduct in the Hopf algebra of motivic iterated integrals. Yamamoto introduced Yamamoto's integral which generalizes iterated integrals and gave a new integral expression for multiple zeta star values using Yamamoto's integral. In this paper, we consider the motivic version of Yamamoto's integral and generalize Goncharov's coproduct formula to those motivic integrals. As an example, we will compute the coproduct of a certain type of Schur multiple zeta values.