Real Algebraic and Analytic Geometry

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113. Bruce Reznick:
On the absence of uniform denominators in Hilbert's 17th problem.


Submission: 2004, June 8.

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.

Full text, 7p.: dvi 31k, ps.gz 139k, pdf 199k.

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