Reciprocity formulae for general multiple Dedekind-Rademacher sums and enumeration of lattice points
Reciprocity laws for generalized higher dimensional Dedekind sums
We define a class of generalized Dedekind sums and prove a family of reciprocity laws for them. These sums and laws generalize those of Zagier [6]. The method is based on that of Solomon [5].
Recurrence formulae for multi-poly-Bernoulli numbers.
Recurrences for the Bernoulli and Euler numbers.
Remarks on sum of products of -twisted Euler polynomials and numbers.
Rota-Baxter operators and Bernoulli polynomials
We develop the connection between Rota-Baxter operators arisen from algebra and mathematical physics and Bernoulli polynomials. We state that a trivial property of Rota-Baxter operators implies the symmetry of the power sum polynomials and Bernoulli polynomials. We show how Rota-Baxter operators equalities rewritten in terms of Bernoulli polynomials generate identities for the latter.