Real Algebraic and Analytic Geometry
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Submission: 2004, January 26.
We consider Hilbert's 17 problem for global analytic functions in a modified form that involves infinite sums of squares. This reveals an essential connection between the solution of the problem and the computation of Pythagoras numbers of meromorphic functions.
Mathematics Subject Classification (2000): 14P99,11E25,32B10.
Keywords and Phrases: Hilbert 17th Problem, Pythagoras number, sum of squares, bad set, germs at closed sets.
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