— Various multiple Dedekind sums were introduced by B.C.Berndt, L.Carlitz, S.Egami, D.Zagier and A.Bayad. In this paper, noticing the Jacobi form in Bayad [4], the cotangent function in Zagier [23], Egami’s result on cotangent functions [14] and their reciprocity laws, we study a special case of the Jacobi forms in Bayad [4] and deduce a generalization of Egami’s result on cotangent functions a...

String functions are important building blocks of characters integrable highest modules over affine Kac--Moody algebras. Kac and Peterson computed string for Lie algebras type $A_{1}^{(1)}$ in terms Dedekind eta functions. We produce new relations between by writing them as double-sums then using certain symmetry relations. evaluate the series special double-sum formulas that express Hecke-type...