Evaluating Generating Functions for Periodic Multiple Polylogarithms
Number Theory
2020-12-08 v1
Abstract
The goal of the paper is to give a systematic way to numerically evaluate the generating function of a periodic multiple polylogarithm using a Chen-Fliess series with a rational generating series. The idea is to realize the corresponding Chen-Fliess series as a bilinear dynamical system. A standard form for such a realization is given. The method is also generalized to the case where the multiple polylogarithm has non-periodic components. This allows one, for instance, to numerically validate the Hoffman conjecture. Finally, a setting in terms of dendriform algebras is provided.
Cite
@article{arxiv.1603.05948,
title = {Evaluating Generating Functions for Periodic Multiple Polylogarithms},
author = {Kurusch Ebrahimi-Fard and W. Steven Gray and Dominique Manchon},
journal= {arXiv preprint arXiv:1603.05948},
year = {2020}
}