On the periodicity of continued fractions in hyperelliptic fields

Abstract

On the basis of a given criterion for the quasi-periodicity of continued fractions for elements of the hyperelliptic field L = K(x)(\(\sqrt f \)), where K is an arbitrary field of characteristic different from 2 and f ∈ K[x] is a square-free polynomial, new polynomials f ∈ Q[x] of odd degree for which the elements of \(\sqrt f \) have periodic continued fraction expansion are found.