### Abstract

In this article, we set up a method of reconstructing the polylogarithms 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-Zamolodchikov equation of one variable as a Riemann-Hilbert problem.

Original language | English |
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Title of host publication | Springer Proceedings in Mathematics and Statistics |

Publisher | Springer New York LLC |

Pages | 491-496 |

Number of pages | 6 |

Volume | 40 |

ISBN (Print) | 9781447148623 |

DOIs | |

Publication status | Published - 2013 |

### ASJC Scopus subject areas

- Mathematics(all)

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## Cite this

Oi, S., & Ueno, K. (2013). The inversion formula of polylogarithms and the riemann-hilbert problem. In

*Springer Proceedings in Mathematics and Statistics*(Vol. 40, pp. 491-496). Springer New York LLC. https://doi.org/10.1007/978-1-4471-4863-0_20