From polygons and symbols to polylogarithmic functions
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Publication:1796034
DOI10.1007/JHEP10(2012)075zbMATH Open1397.81355arXiv1110.0458OpenAlexW3102310584MaRDI QIDQ1796034
Author name not available (Why is that?)
Publication date: 16 October 2018
Published in: (Search for Journal in Brave)
Abstract: We present a review of the symbol map, a mathematical tool that can be useful in simplifying expressions among multiple polylogarithms, and recall its main properties. A recipe is given for how to obtain the symbol of a multiple polylogarithm in terms of the combinatorial properties of an associated rooted decorated polygon. We also outline a systematic approach to constructing a function corresponding to a given symbol, and illustrate it in the particular case of harmonic polylogarithms up to weight four. Furthermore, part of the ambiguity of this process is highlighted by exhibiting a family of non-trivial elements in the kernel of the symbol map for arbitrary weight.
Full work available at URL: https://arxiv.org/abs/1110.0458
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