The inversion formula of polylogarithms and the riemann-hilbert problem

Shu Oi; Kimio Ueno

doi:10.1007/978-1-4471-4863-0_20

The inversion formula of polylogarithms and the riemann-hilbert problem

Shu Oi, Kimio Ueno^*

^*Corresponding author for this work

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

1 Citation (Scopus)

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
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	https://doi.org/10.1007/978-1-4471-4863-0_20
Publication status	Published - 2013

ASJC Scopus subject areas

Mathematics(all)

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

Cite this

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title = "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.",

author = "Shu Oi and Kimio Ueno",

year = "2013",

doi = "10.1007/978-1-4471-4863-0_20",

language = "English",

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AU - Oi, Shu

AU - Ueno, Kimio

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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.

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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 -

The inversion formula of polylogarithms and the riemann-hilbert problem

Abstract

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