A study of elliptic gamma function and allies

We study analytic and arithmetic properties of the elliptic gamma function [formula could not be replicated] in the regime p = q, in particular, its connection with the elliptic dilogarithm and a formula of S. Bloch. We further extend the results to more general products by linking them to non-holomorphic Eisenstein series and, via some formulae of D. Zagier, to elliptic polylogarithms.