On the periodic writing of cubic irrationals and a generalization of Redei functions

摘要

In this paper, we provide a periodic representation (by means of periodic rational or integer sequences) for any cubic irrationality. In particular, for a root alpha of a cubic polynomial with rational coefficients, we study the Cerruti polynomials mu((0))(n) (z), mu((1))(n) (z), and mu((2))(n) (z), which are defined via