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When Newton met Diophantus : A study of rational-derived polynomials and their extension to quadratic fields

MacDougall, James A. and Buchholz, Ralph H. (2000) When Newton met Diophantus : A study of rational-derived polynomials and their extension to quadratic fields. Journal of Number Theory, 81 . pp. 210-233.

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    Abstract

    We consider the problem of classifying all univariate polynomials, de�ned over a domain $k$, with the property that they and all their derivatives have all their roots in $k$. This leads to a number of interesting sub-problems such as finding $k$-rational points on a curve of genus 1 and rational points on a curve of genus 2.

    Item Type: Article
    Subjects: 00-xx General
    Faculty: UNSPECIFIED
    Depositing User: Stephanie
    Date Deposited: 18 Nov 2010 12:10
    Last Modified: 18 Nov 2010 12:10
    URI: https://docserver.carma.newcastle.edu.au/id/eprint/824

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