The algebra of Kleene stars of the plane and polylogarithms
Ngoc Hoang (LIPN), G\'erard Duchamp (LIPN), Hoang Ngoc Minh (LIPN)
TL;DR
This paper explores the algebraic structure of polylogarithms associated with rational series over a specific alphabet, extending their definition and analyzing their properties.
Contribution
It introduces an extended framework for the algebraic study of polylogarithms related to Kleene stars of the plane.
Findings
Defined new algebraic properties of polylogarithms
Extended the class of rational series for polylogarithm analysis
Provided insights into the algebraic structure of polylogarithms
Abstract
We extend the definition and study the algebraic properties of the polylogarithm Li(T), where T is rational series over the alphabet X = {x 0, x 1} belonging to suitable subalgebras of rational series.
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Taxonomy
TopicsAdvanced Mathematical Identities · Advanced Combinatorial Mathematics · Analytic Number Theory Research