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

Matthes, Nils; Tasaka, Koji

doi:10.2206/kyushujm.73.337

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

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Matthes, Nils
Max Planck Institute for Mathematics, Max Planck Society;

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Tasaka, Koji
Max Planck Institute for Mathematics, Max Planck Society;

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https://doi.org/10.2206/kyushujm.73.337
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arXiv:1805.09500.pdf
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Matthes-Tasaka_On Ecalles and Browns polar solutions to the double shuffle equations_2019.pdf
(Publisher version), 236KB

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Citation

Matthes, N., & Tasaka, K. (2019). On Ecalle's and Brown's polar solutions to the double shuffle equations modulo products. Kyushu Journal of Mathematics, 73(2), 337-359. doi:10.2206/kyushujm.73.337.

Cite as: https://hdl.handle.net/21.11116/0000-0006-BBD6-6

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.