Integer points and models of algebraic curves
type: Item
instance of: scholarly article
title: Integer points and models of algebraic curves
zbMATH Open document ID: 0811.11023
DOI: 10.1007/BF01305778
author: Dimitros Poulakis
published in: Monatshefte für Mathematik
publication date: 1994-10-09T00:00:00Z
full work available at URL: https://eudml.org/doc/178661
review text: This paper describes a method for the construction of models of algebraic curves \(F(X, Y)=0\) of genus \(\geq 1\) defined over a number field, and the effective computation of integer points on such models. This construction is applied to the problem of the effective determination of integer points on curves of genus 2 by reducing this problem to that of effectively computing integer points on quartic equations defined over a number field. The results obtained are also applied to give explicit upper bounds for the heights of integer points on a family of curves \(F(X, Y)=0\) defined over a number field, which are cyclic coverings of the projective line.
Mathematics Subject Classification ID: 11D25
Mathematics Subject Classification ID: 11G30
zbMATH DE Number: 650853
zbMATH Keywords: global field
zbMATH Keywords: algebraic curves
zbMATH Keywords: effective computation of integer points
zbMATH Keywords: integer points on curves of genus 2
zbMATH Keywords: integer points on quartic equations
zbMATH Keywords: explicit upper bounds for the heights of integer points
zbMATH Keywords: cyclic coverings
reviewed by: Roelof J. Stroeker
MaRDI profile type: Publication
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OpenAlex ID: W123290555
description: scientific article; zbMATH DE number 650853