Iterated integrals on P1∖{0,1,∞,z} and a class of relations among multiple zeta

The motivic Galois group of mixed Tate motives over $\mathbb{Z}[1/2]$ and its action on the fundamental group of $\mathbb{P}^{1}\setminus\{0,\pm1,\infty\}$

“…Remark 6.22. Theorem 6.21 can be viewed as an ultimate generalization of the confluence relation defined in the authors' previous paper [11]. In fact, the confluence relation in [11] is obtained from Theorem 6.21 under the setting P := {0, 1, z} and S := {0, 1} together with the tangential vectors v(0) = 1, v(1) = −1.…”

“…. , p k+1 ∈ {0, 1, z} with p 0 = 0, p k+1 = 1 gives relations among multiple zeta values, which was discussed in the authors' previous paper [11], which was later proved to be equivalent to Drinfeld's pentagon equation of the KZ-associator by Furusho [8]. In this paper, we focus on another case where x = 0, y = 1, p 0 , .…”

Algebraic differential formulas for the shuffle, stuffle and duality relations of iterated integrals

“…For example, in [8], the authors proved a "sum formula" for iterated integrals, which generalizes the classical sum formula for MZVs, by using its inductive structure with respect to the algebraic differentiation. Also, in [9], the authors exploited the differential structure of A 0…”

On a basis for Euler-Zagier double zeta functions with non-positive components

“…In particular, the algebraic structure of MZV has been widely studied, and many kinds of algebraic relations over Q are known. The algebraic relations such as Extended double shuffle relation ( [10]), associator relation ( [5]), confluence relation ( [8]), and Kawashima's relation ( [11]) are expected to exhaust all relations of MZVs, respectively. Note that some relations among MZVs are generalized to MZFs (see [6,7,15], for example).…”