Resumen de Periodic continued fractions and hyperelliptic curves

M. P. Grosset, Alexander P. Veselov

• We investigate when an algebraic function of the form ()=(�B()+R())/A(), where R() is a polynomial of odd degree N=2g+1 with coefficients in , can be written as a periodic -fraction of the form for some fixed sequence i. We show that this problem has a natural answer given by the classical theory of hyperelliptic curves and their Jacobi varieties. We also consider pure periodic -fraction expansions corresponding to the special case when bN=b0.