Arithmetic of quadratic fields and torsion in Jacobians
type: Item
instance of: scholarly article
title: Arithmetic of quadratic fields and torsion in Jacobians
zbMATH Open document ID: 1217.11094
DOI: 10.1134/S1064562410010163
published in: Doklady Mathematics
publication date: 2010-11-17T00:00:00Z
review text: Let \(K\) be an algebraic number field, \(f(x)=x^{2n}+a_{2n-1}x^{2n-1}+\ldots+a_0\in K[X]\) a squarefree polynomial, \[ D_f=K[X](\sqrt{f})=\{\alpha+\beta\sqrt{f}\mid \alpha,\beta\in K[X]\}. \] The author formulates a local-global principle for the existence of nontrivial units in \(D_f\).
reviewed by: Florin Nicolae
Mathematics Subject Classification ID: 11R09
Mathematics Subject Classification ID: 11R27
Mathematics Subject Classification ID: 11R11
zbMATH DE Number: 5816860
zbMATH Keywords: units
zbMATH Keywords: local-global principle
author: V. P. Platonov
MaRDI profile type: Publication
cites work: Multiples of Points on Elliptic Curves and Continued Fractions
cites work: Bounds for the torsion of elliptic curves over number fields
cites work: Rational isogenies of prime degree. (With an appendix by D. Goldfeld)
cites work: Groups of \(S\)-units in hyperelliptic fields
cites work: Continued fractions and \(S\)-units in function fields
description: scientific article; zbMATH DE number 5816860