Real Algebraic and Analytic Geometry |
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Submission: 2004, September 28.
Abstract:
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.
Full text, 32p.: dvi 147k, ps.gz 196k, pdf 305k.