On the pythagoras numbers of real analytic set germs.



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Fernando Galván, José Francisco and Ruiz Sancho, Jesús María (2005) On the pythagoras numbers of real analytic set germs. Bulletin de la Société Mathématique de France, 133 (3). pp. 349-362. ISSN 0037-9484

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Official URL: http://smf.emath.fr/en/Publications/Bulletin/


We Show that (i) the Pythagoras number of a real analytic set germ is the supremum of the Pythagoras numbers of the curve germs it contains, and (ii) every real analytic curve germ is contained in a real analytic surface germ with the same Pythagoras number (or Pythagoras number 2 if the curve is Pythagorean). This gives new examples and counterexamples concerning sums of squares and positive semidefinite analytic function germs.

Item Type:Article
Uncontrolled Keywords:Pythagoras number; sum of squares; M. Artin’s approximation.
Subjects:Sciences > Mathematics > Algebraic geometry
ID Code:15159
Deposited On:10 May 2012 09:04
Last Modified:09 Aug 2018 08:03

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