Generalized Rademacher functions and some congruence properties

In 1, we introduce the classical Dedekind sum and the Rademacher function. Then, in 2, certain generalized Rademacher functions are introduced as the Eichler-Shimura type period integrals of Eisenstein series. In 3, we present a version of continued fraction algorithm which computes efficiently the generalized Rademacher functions. In 4, we show a congruence formula connecting values of the generalized Rademacher functions of weight 2 and weight k > 2. This formula will be applied in a forthcoming paper [N4].