Multiple Elliptic Polylogarithms

Francis C. S. Brown; Andrey Levin

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arXiv · 1110.6917

Multiple Elliptic Polylogarithms

Francis C. S. Brown·Andrey Levin

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Abstract

We study the de Rham fundamental group of the configuration space $E^{(n)}$ of $n+1$ marked points on an elliptic curve $E$, and define multiple elliptic polylogarithms. These are multivalued functions on $E^{(n)}$ with unipotent monodromy, and are constructed by a general averaging procedure. We show that all iterated integrals on $E^{(n)}$, and in particular the periods of the unipotent fundamental group of the punctured curve $E \backslash \{0\}$, can be expressed in terms of these functions.

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Francis C. S. Brown, Andrey Levin. 2013-06-20. Multiple Elliptic Polylogarithms. https://arxiv.org/abs/1110.6917

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