Continued rational fractions in hyperelliptic fields and the Mumford representation

Abstract

A relationship between the continued fraction expansion of the quadratic irrationalities of hyperelliptic fields and the Mumford polynomials determining addition in the group of divisor classes on a hyperelliptic curve is described. A theorem on the equivalence of the quasi-periodicity of a quadratic irrationality and the existence of a point of finite order is proved; results on the symmetry of the quasi-period and estimates of its length are obtained.