Multiple elliptic Apostol-Dedekind-Zagier sums

Multiple elliptic Apostol-Dedekind-Zagier sums. Let tau epsilon H (= upper half plane). We introduce an elliptic analogue of the classical Dedekind-Zagier multiple sums [Zagier, Math. Ann. 202 (1973) 149-172] and Apostol sums [Apostol, Duke Math. J. 17 (1950) 147-157]. These sums are defined by means of certain Jacobi modular forms of two variables D, (z; o). We prove a reciprocity law for these elliptic sums, which gives new relations between some modular Jacobi forms of two variables.