Real Algebraic and Analytic Geometry |

On the absence of uniform denominators in Hilbert's 17th problem.

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Submission: 2004, June 8.

*Abstract:
Text: Suppose (n,d) is such that there exist positive
semidefinite forms p of degree d in n variables which are not a sum of
squares. We show that there does not exist a finite set of non-zero forms
H so that if p is positive semidefinite, then h*p is a sum of squares of
forms for some h in H. This paper will appear in the Proceedings of
the American Mathematical Society.*

Mathematics Subject Classification (2000): 11E76, 11E25.

Keywords and Phrases: Hilbert's 17th problem, denominators, sums of squares.

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