Overview on elliptic multiple zeta values. (English) Zbl 1444.81035
Burgos Gil, José Ignacio (ed.) et al., Periods in quantum field theory and arithmetic. Outcome of the “Research Trimester on Multiple Zeta Values, Multiple Polylogarithms, and Quantum Field Theory”, ICMAT 2014, Madrid, Spain, September 15–19, 2014. Cham: Springer. Springer Proc. Math. Stat. 314, 105-132 (2020).
Summary: 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.
For the entire collection see [Zbl 1446.81002].
For the entire collection see [Zbl 1446.81002].
MSC:
| 81T40 | Two-dimensional field theories, conformal field theories, etc. in quantum mechanics |
| 11M32 | Multiple Dirichlet series and zeta functions and multizeta values |
| 11G55 | Polylogarithms and relations with \(K\)-theory |
| 11G05 | Elliptic curves over global fields |
| 11M35 | Hurwitz and Lerch zeta functions |
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