### 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 |

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### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

*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

**The inversion formula of polylogarithms and the riemann-hilbert problem.** / Oi, Shu; Ueno, Kimio.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

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

}

TY - GEN

T1 - The inversion formula of polylogarithms and the riemann-hilbert problem

AU - Oi, Shu

AU - Ueno, Kimio

PY - 2013

Y1 - 2013

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84883389328&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84883389328&partnerID=8YFLogxK

U2 - 10.1007/978-1-4471-4863-0_20

DO - 10.1007/978-1-4471-4863-0_20

M3 - Conference contribution

AN - SCOPUS:84883389328

SN - 9781447148623

VL - 40

SP - 491

EP - 496

BT - Springer Proceedings in Mathematics and Statistics

PB - Springer New York LLC

ER -