Theorems on generalized Dedekind sums

were introduced by the author [l]. The integers h and k are assumed relatively prime, Bp(x) is the p-th Bernoulli function, Bp (x) the p-th Bernoulli polynomial (for definitions see [l;(2.11), (2.12)]), and [x] is the greatest integer < ̂ x. For even values of the integer p the sums (1) are trivial (see [l; (4.13)1) and w