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arXiv · 1112.0389

The inversion formula of polylogarithms and the Riemann-Hilbert problem

Shu Oi·Kimio Ueno
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Abstract

In this article, we set up a method of reconstructing to polylogarithms $\mathrm{Li}_k(z)$ 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-Zamolodochikov equation of one variable as a Riemann-Hilbert problem.

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Shu Oi, Kimio Ueno. 2012-03-14. The inversion formula of polylogarithms and the Riemann-Hilbert problem. https://arxiv.org/abs/1112.0389

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