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Evaluating Generating Functions for Periodic Multiple Polylogarithms
- Source :
- Periods in Quantum Field Theory and Arithmetic. Springer Proceedings in Mathematics & Statistics, vol 314, 2020
- Publication Year :
- 2016
-
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.
- Subjects :
- Mathematics - Number Theory
Subjects
Details
- Database :
- arXiv
- Journal :
- Periods in Quantum Field Theory and Arithmetic. Springer Proceedings in Mathematics & Statistics, vol 314, 2020
- Publication Type :
- Report
- Accession number :
- edsarx.1603.05948
- Document Type :
- Working Paper
- Full Text :
- https://doi.org/10.1007/978-3-030-37031-2_17