Analogues of Dedekind sums

In this work, transformation formulas under modular substitutions are obtained for a large class of generalized Eisenstein series. Appearing in the transformation formulae are generalizations of Dedekind sums involving the periodic Bernoulli function. Reciprocity theorems are proved for these Dedekind sums. Furthermore, these sums for some special cases are considered. As applications of the transformation formulae, relations between various infinite series and analogues of Ramanujan's formula for periodic zeta functions are derived.