Abstract
In this article, we set up a method of reconstructing the polylogarithms \(\operatorname {Li}_{k}(z)\) 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.
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References
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Acknowledgements
The first author is supported by Waseda University Grant for Special Research Projects No. 2011B-095. The second author is partially supported by JSPS Grant-in-Aid No. 22540035.
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Dedicated to Professor Michio Jimbo.
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Oi, S., Ueno, K. (2013). The Inversion Formula of Polylogarithms and the Riemann-Hilbert Problem. In: Iohara, K., Morier-Genoud, S., Rémy, B. (eds) Symmetries, Integrable Systems and Representations. Springer Proceedings in Mathematics & Statistics, vol 40. Springer, London. https://doi.org/10.1007/978-1-4471-4863-0_20
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DOI: https://doi.org/10.1007/978-1-4471-4863-0_20
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