English

On Ecalle's and Brown's polar solutions to the double shuffle equations modulo products

Number Theory 2019-09-24 v2

Abstract

Two explicit sets of solutions to the double shuffle equations modulo products were introduced by Ecalle and Brown respectively. We place the two solutions into the same algebraic framework and compare them. We find that they agree up to and including depth four but differ in depth five by an explicit solution to the linearized double shuffle equations with an exotic pole structure.

Keywords

Cite

@article{arxiv.1805.09500,
  title  = {On Ecalle's and Brown's polar solutions to the double shuffle equations modulo products},
  author = {Nils Matthes and Koji Tasaka},
  journal= {arXiv preprint arXiv:1805.09500},
  year   = {2019}
}

Comments

22 pages, final version, to appear in Kyushu J. Math