Overview on elliptic multiple zeta values

Conference item

We give an overview of some work on elliptic multiple zeta values. First defined by Enriquez as the coefficients of the elliptic KZB associator, elliptic multiple zeta values are also special values of multiple elliptic polylogarithms in the sense of Brown and Levin. Common to both approaches to elliptic multiple zeta values is their representation as iterated integrals on a once-punctured elliptic curve. Having compared the two approaches, we survey various recent results about the algebraic structure of elliptic multiple zeta values, as well as indicating their relation to iterated integrals of Eisenstein series, and to a special algebra of derivations.

Authors: Matthes, N

• Publication status: Published
• Peer review status: Peer reviewed
• Publisher: Springer Nature
• Host title: Springer Proceedings in Mathematics and Statistics
• Journal: Springer Proceedings in Mathematics & Statistics
• Volume: 314
• Pages: 105-132
• Publication date: 2020-03-14
• Acceptance date: 2017-04-25
• Event title: ICMAT-MZV 2014: Periods in Quantum Field Theory and Arithmetic
• Event series: Workshop Research Trimester on Multiple Zeta Values, Multiple Polylogarithms, and Quantum Field Theory
• Event location: ICMAT, Madrid, Spain
• Event website: https://link.springer.com/bookseries/10533
• Event start date: 2014-09-01
• Event end date: 2014-12-31
• DOI: 10.1007/978-3-030-37031-2_5
• EISSN: 2194-1017
• ISSN: 2194-1009
• EISBN: 978-3-030-37031-2
• ISBN: 978-3-030-37030-5
• Language: English
• Keywords: elliptic KZB equation; FFR; elliptic multiple zeta values; multiple elliptic polylogarithms