On the parametrization of hyperelliptic fields with \(S\)-units of degrees 7 and 9
type: Item
instance of: scholarly article
title: On the parametrization of hyperelliptic fields with \(S\)-units of degrees 7 and 9
DOI: 10.1134/S0001434622090139
author: G. V. Fedorov
author: Vladimir S. Zhgoon
author: M. M. Petrunin
author: Yu. N. Shteĭnikov
published in: Mathematical Notes
publication date: 2022-10-25T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 11J70
Mathematics Subject Classification ID: 11R58
Mathematics Subject Classification ID: 11R27
Mathematics Subject Classification ID: 13P10
zbMATH DE Number: 7606791
zbMATH Keywords: hyperelliptic field
zbMATH Keywords: torsion point
zbMATH Keywords: rational curve
zbMATH Keywords: Gröbner basis
reviewed by: Vijay Yadav
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 7606791