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Mathematics > Number Theory

arXiv:1805.09500 (math)
[Submitted on 24 May 2018 (v1), last revised 23 Sep 2019 (this version, v2)]

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

Authors:Nils Matthes, Koji Tasaka
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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.
Comments: 22 pages, final version, to appear in Kyushu J. Math
Subjects: Number Theory (math.NT)
MSC classes: 11M32 (17B01)
Cite as: arXiv:1805.09500 [math.NT]
  (or arXiv:1805.09500v2 [math.NT] for this version)
  https://doi.org/10.48550/arXiv.1805.09500

Submission history

From: Nils Matthes [view email]
[v1] Thu, 24 May 2018 04:04:51 UTC (20 KB)
[v2] Mon, 23 Sep 2019 09:55:14 UTC (20 KB)
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