Continued fractions and \(S\)-units in function fields
type: Item
instance of: scholarly article
title: Continued fractions and \(S\)-units in function fields
zbMATH Open document ID: 1221.11224
DOI: 10.1134/S1064562408060082
author: V. V. Benyash-Krivets
author: V. P. Platonov
published in: Doklady Mathematics
publication date: 2011-06-08T00:00:00Z
review text: Let \(k\) be an arbitrary field, \(k(x)\) the rational function field, \(\nu\in k[x]\) a polynomial of degree \(1\), \(k(x)_\nu\) the completion at \(\nu\), \(\beta\in k(x)_\nu\). The authors prove that if a fraction \(\frac ab\in k(x)\) is a best approximation to \(\beta \), then there exists a convergent \(\frac{p_n}{q_n}\) of \(\beta\) and a constant \(c\in k^*\) such that \(a=cp_n\) and \(b=cq_n\). They show how continued fractions can be applied to find fundamental \(S\)-units in hyperelliptic fields.
reviewed by: Florin Nicolae
Mathematics Subject Classification ID: 11R58
Mathematics Subject Classification ID: 11J70
zbMATH DE Number: 5905451
zbMATH Keywords: function field
zbMATH Keywords: continued fraction
MaRDI profile type: Publication
cites work: Multiples of Points on Elliptic Curves and Continued Fractions
cites work: Q5566639
cites work: Groups of \(S\)-units in hyperelliptic fields
description: scientific article; zbMATH DE number 5905451