· 2016· Preprint
From polygons and symbols to polylogarithmic functions
- 189citations
- 2016year
Short summary
A review introduces the symbol map, a tool for simplifying polylogarithm expressions, linking them to combinatorial properties of decorated polygons.
AI-generated from the title and abstract; the full text is not read.
Key points
- The symbol map simplifies expressions among multiple polylogarithms.
- Symbols of polylogarithms can be derived from combinatorial properties of rooted decorated polygons.
- A systematic approach is presented for constructing functions from symbols, illustrated for harmonic polylogarithms.
- Non-trivial elements in the kernel of the symbol map are exhibited, indicating ambiguity.
AI-generated from the title and abstract; the full text is not read.
Abstract
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 illus-trate 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.
The authors' abstract, as published at the source., 2016 · DOI ↗
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Field: Algebra and Number Theory
Algebra and Number TheoryMathematics