The inversion formula of polylogarithms and the riemann-hilbert problem

Abstract

In this article, we set up a method of reconstructing the polylogarithms Lik(z) from zeta values ζ(k) via the Riemann-Hilbert problem. This is referred to as "a recursive Riemann-Hilbert problem of additive type." Moreover, we suggest a framework of interpreting the connection problem of the Knizhnik-Zamolodchikov equation of one variable as a Riemann-Hilbert problem. © Springer-Verlag London 2013.