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arXiv · 1110.0458

From polygons and symbols to polylogarithmic functions

Claude Duhr·Herbert Gangl·John R. Rhodes
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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.

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Claude Duhr, Herbert Gangl, John R. Rhodes. 2011-10-03. From polygons and symbols to polylogarithmic functions. https://doi.org/10.1007/jhep10(2012)075

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