Real Algebraic and Analytic Geometry |

On the Pythagoras number of real analytic surfaces.

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Submission: 2004, June 9.

*Abstract:
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.

**Full text**, 31p.:
pdf 246k.

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