ИСТИНА

The paper [1] raised the question of the finiteness of the number squarefree polynomials f∈Q[h] of fixed degree with periodic continued fraction expansion of f−−√ in the field Q((h)), for which the fields Q(h)(f−−√) are not isomorphic to one another and to fields of the form Q(h)(chn+1−−−−−−√), where c∈Q∗, n∈N. In the joint paper, V.P. Platonov and G.V. Fedorov [2] obtained a positive answer to this question for elliptic fields Q(h)(f−−√), degf=3. The report will present the results of the article [2]. [1] V.P. Platonov, G.V. Fedorov, On the periodicity of continued fractions in elliptic fields. Doklady Mathematics. 2017 (to appear). [2] V.P. Platonov, G.V. Fedorov, On the periodicity of continued fractions in hyperelliptic fields. Doklady Mathematics. 2017 (to appear).