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Evaluating Generating Functions for Periodic Multiple Polylogarithms via Rational Chen–Fliess Series

  • Kurusch Ebrahimi-Fard
  • W. Steven GrayEmail author
  • Dominique Manchon
Conference paper
  • 32 Downloads
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 314)

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.

Keywords

Chen–Fliess series Dendriform algebra Hoffman conjecture Multiple polylogarithms Rational formal power series 

Notes

Acknowledgements

The second author was supported by grant SEV-2011-0087 from the Severo Ochoa Excellence Program at the Instituto de Ciencias Matemáticas in Madrid, Spain. This research was also supported by a grant from the BBVA Foundation.

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Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  • Kurusch Ebrahimi-Fard
    • 1
  • W. Steven Gray
    • 2
    Email author
  • Dominique Manchon
    • 3
  1. 1.Department of Mathematical SciencesNorwegian University of Science and Technology (NTNU)TrondheimNorway
  2. 2.Old Dominion UniversityNorfolkUSA
  3. 3.LMBPCNRS - Université Clermont-AuvergneAubière CedexFrance

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