On the number of \(S\)-integral solutions to \(Y^m = f(X)\)
type: Item
instance of: scholarly article
title: On the number of \(S\)-integral solutions to \(Y^m = f(X)\)
zbMATH Open document ID: 0816.11022
DOI: 10.1007/BF01292773
author: Paul Voutier
published in: Monatshefte für Mathematik
publication date: 1995-04-02T00:00:00Z
full work available at URL: https://eudml.org/doc/178678
review text: Let \(K\) be an algebraic number field, \(m\) an integer \(\geq 2\) and \(f(X)\) a non-zero polynomial with coefficients in \(K\). In 1986 \textit{J. H. Evertse} and \textit{J. Silverman} established the first explicit upper bound on the number of \(S\)-integral solutions to the equation \(Y^m= f(X)\), under some necessary and sufficient conditions for the curve described by this equation to be of positive genus [Math. Proc. Camb. Philos. Soc. 100, 237--248 (1986; Zbl 0611.10009)]. In the paper under review the author, using the method of Evertse and Silverman, gives some refinements and generalizations of their results. Also, a conjecture of Schmidt, in some particular cases, is proved.
reviewed by: Dimitros Poulakis
Mathematics Subject Classification ID: 11D41
zbMATH DE Number: 733135
zbMATH Keywords: hyperelliptic equation
zbMATH Keywords: superelliptic equation
zbMATH Keywords: \(S\)-integral solutions
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 733135