Real Algebraic and Analytic Geometry |

On the Hilbert 17th Problem for Global Analytic Functions.

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Submission: 2004, January 26.

*Abstract:
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.

**Full text**, 31p.:
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