Preprint 2019-03
Johannes Brödel, André Kaderli
Functional relations for elliptic polylogarithms.
Abstract: Numerous examples of functional relations for multiple polylogarithms are known. For elliptic polylogarithms, however, tools for the exploration of func- tional relations are available, but only very few relations are identified. Starting from an approach of Zagier and Gangl, which in turn is based on con- siderations about an elliptic version of the Bloch group, we explore functional relations between elliptic polylogarithms and link them to the relations which can be derived using the elliptic symbol formalism. The elliptic symbol formal- ism in turn allows for an alternative proof of the validity of the elliptic Bloch relation.
While the five-term identity is the prime example of a functional identity for multiple polylogarithms and implies many dilogarithm identities, the situation in the elliptic setup is more involved: there is no simple elliptic analogue, but rather a whole class of elliptic identities.
Preprint series: Institut für Mathematik, Humboldt-Universität zu Berlin (ISSN 0863-0976), 2019-03
53 pp.