Real Algebraic and Analytic Geometry

114. Francesca Acquistapace, Fabrizio Broglia, José F. Fernando, Jesús M. Ruiz:
On the Pythagoras number of real analytic surfaces.

e-mail: , , ,

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.

Server Home Page