Hilbert’s Seventeenth Problem and Hyperelliptic Curves
نویسنده
چکیده
This article deals with a constructive aspect of Hilbert’s seventeenth problem : producing a collection of real polynomials in two variables of degree 8 in one variable which are positive but are not a sum of three squares of rational fractions. To do this we use a reformulation of this problem in terms of hyperelliptic curves due to Huisman and Mahé and we follow a method from Cassels, Ellison and Pfister which involves the computation of a Mordell-Weil rank over R(x).
منابع مشابه
Using hyperelliptic curves to find posi - tive polynomials that are not sum of three squares in
This article deals with a quantitative aspect of Hilbert’s seventeenth problem : producing a collection of real polynomials in two variables of degree 8 in one variable which are positive but are not a sum of three squares of rational fractions. As explained by Huisman and Mahé, a given monic squarefree positive polynomial in two variables x and y of degree in y divisible by 4 is a sum of three...
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تاریخ انتشار 2007