On the problem of periodicity of continued fraction expansions of for cubic polynomials over algebraic number fields

Abstract

We obtain a complete description of the fields that are extensions of of degree at most and the cubic polynomials such that the expansion of into a continued fraction in the field of formal power series is periodic. We prove a finiteness theorem for cubic polynomials with a periodic expansion of for extensions of of degree at most . We obtain a description of the periodic elements for the cubic polynomials defining elliptic curves with points of order , . Bibliography: 19 titles.