Universidad Complutense de Madrid
E-Prints Complutense

On the finiteness of Pythagoras numbers of real meromorphic functions.

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Acquistapace, Francesca y Broglia, Fabrizio y Fernando Galván, José Francisco y Ruiz Sancho, Jesús María (2010) On the finiteness of Pythagoras numbers of real meromorphic functions. Bulletin de la Société Mathématique de France , 138 (2). pp. 231-247. ISSN 0037-9484

URL Oficial: http://cat.inist.fr/?aModele=afficheN&cpsidt=22896755



Resumen

We consider the 17(th) Hilbert Problem for global real analytic functions in a modified form that involves infinite sums of squares. Then we prove a local-global principle for a real global analytic function to be a sum of squares of global real meromorphic functions. We deduce that an affirmative solution to the 17(th) Hilbert Problem for global real analytic functions implies the finiteness of the Pythagoras number of the field of global real meromorphic functions, hence that of the field of real meromorphic power series. This measures the difficulty of the 17(th) Hilbert problem in the analytic case.


Tipo de documento:Artículo
Palabras clave:17th Hilbert problem; Pythagoras number; Sum of squares; Bad set; Germs
Materias:Ciencias > Matemáticas > Geometria algebraica
Código ID:15094
Depositado:04 May 2012 11:41
Última Modificación:14 May 2013 13:31

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