Multiple Elliptic Polylogarithms
185 citations recorded by the source corpus.
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.
Subfields: Algebra and Number Theory, Applied Mathematics
View Paper: https://www.semanticscholar.org/paper/eb524577f55e981d21af722eeaa841cab644083a
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In Algebra and Number Theory
- J. Henn
- F. Brown
- Erik Panzer
- Claude Duhr
- Oliver Schnetz
- Gudrun Heinrich
- Falko Dulat
- Thomas Willwacher
In Applied Mathematics
- V. Duca
- Hjalte Frellesvig
- J. Henn
- Vladimir A. Smirnov
- F. Brown
- Erik Panzer
- Gudrun Heinrich
- Claude Duhr
Citations in the corpus
- A class of non-holomorphic modular forms I (2017, background): “nition of the space MIE. A rigorous proof of the relation between closed superstring amplitudes and our class MIE might go along the broad lines of the author’s thesis, generalised to genus one using [3]. 1.3. Acknowledgements. Many thanks to Michael Green, Eric d’Hoker, Pierre Vanhove, Don Zagier a”
- Two-loop planar master integrals for Higgs → 3 partons with full heavy-quark mass dependence (2016, result): “See [62, 63, 67, 85] for results in terms of elliptic polylogarithms [86], and [64–66, 69] for a related class of functions.”
- Analogues elliptiques des nombres multiz\'etas (2013, unknown): “Signalons enfin les liens possibles entre le présent travail et [1] : les auteurs C Z Z Ils projettent d’en déduire, par spécialisation, des fonctions de τ qu’ils appellent”