Real Algebraic and Analytic Geometry
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Submission: 2004, June 9.
We show that (i) every positive semidefinite meromorphic function germ on a surface is a sum of 4 squares of meromorphic function germs, and that (ii) every positive semidefinite global meromorphic function on a normal surface is a sum of 5 squares of global meromorphic functions.
Mathematics Subject Classification (2000): 14P99, 11E25, 32B10, 32S05.
Keywords and Phrases: Pythagoras number, sum of squares, analytic surface germ, global analytic coherent surface, isolated singularity.
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