Monomial Dynamical Systems of Dimension One over Finite Fields

In this paper we study the monomial dynamical systems of dimension one over finite fields from the viewpoints of arithmetic and graph theory. We give formulas for the number of periodic points with period r and cycles with length r. Then we compute the natural distributions of periodic points and cycles. We also define and compute the Dirichlet distributions of periodic points and cycles. Especially, we associate the monomial dynamical systems with function fields to compute distributions.Comment: Accepted by Acta Arithmetica. (SCI

On hypergeometric Bernoulli numbers and polynomials

In this note, we shall provide several properties of hypergeometric Bernoulli numbers and polynomials, including sums of products identity, differential equations and recurrence formulas.Comment: 12 page