Iterated integrals associated with colored rooted trees

Abstract

In this paper, we introduce iterated integrals associated with colored rooted trees and give proofs for the shuffle relations for $\mathbf{p}$-adic finite and $t$-adic symmetric polylogarithms. This method generalizes the theory of the finite multiple zeta values associated with $2$-colored rooted trees introduced by Ono.

23 pages