Fundamental solutions of the Knizhnik-Zamolodchikov equation of one variable and the Riemann-Hilbert problem (Q1989639)

In a previous paper [Springer Proc. Math. Stat. 40, 491--496 (2013; Zbl 1331.11068)], the authors showed that the polylogarithms $Li_k(z)$ are characterized as the unique holomorphic functions on a complex half-plane satisfying the inversion formulas for polylogarithms under certain asymptotic and normalization conditions. \par In the paper under review, a similar problem is solved for multiple polylogarithms of a single variable. The main tool for the inversion formulas for this case (which contain multiple zeta values) is the fundamental system of solutions of the Knizhnik-Zamolodchikov differential equation. Characterizations of these solutions in terms of the additive and multiplicative Riemann-Hilbert problems are given.