Real Algebraic and Analytic Geometry
Submission: 2004, September 28.
This paper extends previous works by Cassels-Ellison-Pfister and Christie in producing different collections of positive polynomials in two variables over the reals which are not sums of three squares of rational fractions. The results are essentially obtained in extending methods of Galois descent for positivity of the rank of special kinds of elliptic curves.
Mathematics Subject Classification (2000): 11E25.
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