Sommes de trois carrés de fractions en deux variables

This paper extends previous works by Cassels-Ellison-Pfister and Christie in producing different collections of positive polynomials in ℝ[X,Y] 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...

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Bibliographic Details
Published in:Manuscripta mathematica 2005-04, Vol.116 (4), p.421-447
Main Authors: Macé, Olivier, Mahé, Louis
Format: Article
Language:English
Online Access:Get full text
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Summary:This paper extends previous works by Cassels-Ellison-Pfister and Christie in producing different collections of positive polynomials in ℝ[X,Y] 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 ℝ(X)-rank of special kinds of elliptic curves.
ISSN:0025-2611
1432-1785
DOI:10.1007/s00229-004-0535-0