On the Pythagoras numbers of real analytic surfaces |
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| Authors: | Francesca Acquistapace |
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| Affiliation: | Dipartimento di Matematica, Università degli Studi di Pisa, Via Filippo Buonarroti, 2, 56127 Pisa, Italy; Dipartimento di Matematica, Università degli Studi di Pisa, Via Filippo Buonarroti, 2, 56127 Pisa, Italy; Departamento de Matemáticas, Facultad de Ciencias, Universidad Autónoma de Madrid, Cantoblanco, 28040 Madrid, Spain; Departamento de Geometría y Topología, Facultad de Ciencias Matemáticas, Universidad Complutense de Madrid, 28040 Madrid, Spain |
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| 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. |
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