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High Energy Physics - Theory, hep-th,Mathematics, Number Theory, math.NT
Abstract:
Numerous examples of functional relations for multiple polylogarithms are
known. For elliptic polylogarithms, however, tools for the exploration of
functional relations are available, but only very few relations are identified.
Starting from an approach of Zagier and Gangl, which in turn is based on
considerations 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 formalism 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.
