On the parametrization of hyperelliptic fields with \(S\)-units of degrees 7 and 9
Based on authors' abstract: This paper shows that if \(k\) is an algebraically closed field with \(\operatorname{char}k=0\), then the set of polynomials \(f\) of degree 5 such that the field \(k(x)(\sqrt{f}\,)\) has a nontrivial \(S\)-unit of degree 7 or 9 and the continued fraction expansion of \(\sqrt{f}/x\) is periodic is a one-parameter set corresponding to a rational curve with finitely many deleted points. In this paper the authors established two theorems and explain its proofs with the help of different types of proposition and definition.
scientific article; zbMATH DE number 7606791
scientific article