# Using hyperelliptic curves to find positive polynomials that are not sum of three squares in R(x, y)

arXiv: Number Theory, 2007.

Keywords:

algebraic geometryhyperelliptic curvenumber theory

Abstract:

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 Mahe, a given monic squarefree positive
polynomial in two variabl...More

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