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The meta-abelian elliptic KZB associator and periods of Eisenstein series

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Abstract

We compute the image of Enriquez’ elliptic KZB associator in the (maximal) meta-abelian quotient of the fundamental Lie algebra of a once-punctured elliptic curve. Our main result is an explicit formula for this image in terms of Eichler integrals of Eisenstein series, and is analogous to Deligne’s computation of the depth one quotient of the Drinfeld associator. We also show how to retrieve Zagier’s extended period polynomials of Eisenstein series, as well as the values at zero of Beilinson–Levin’s elliptic polylogarithms from the meta-abelian elliptic KZB associator.

Keywords

Modular symbols Elliptic associators Elliptic polylogarithms 

Mathematics Subject Classification

11F67 
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© The Author(s) 2017

Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

Authors and Affiliations

  1. 1.Max-Planck-Institut für MathematikBonnGermany

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