Complutense University Library

On the pythagoras numbers of real analytic surfaces


Acquistapace, Francesca and Broglia, Fabrizio and Fernando Galván, José Francisco and Ruiz Sancho, Jesús María (2005) On the pythagoras numbers of real analytic surfaces. Annales Scientifiques de l'École Normale Supérieure. Quatrième Série, 38 (5). pp. 751-772. ISSN 0012-9593

[img] PDF
Restringido a Repository staff only hasta 2020.


Official URL:


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.

Item Type:Article
Uncontrolled Keywords:Pythagoras number; Analytic function; Analytic function germ; Meromorphic function; Meromorphic function germ
Subjects:Sciences > Mathematics > Algebraic geometry
ID Code:15149

ACQUISTAPACE F., BROGLIA F., FERNANDO J.F., RUIZ J.M., On the 17th Hilbert Problem for global analytic functions, Preprint RAAG 2004.

ANDRADAS C., DÍAZ-CANO A., RUIZ J.M., The Artin–Lang property for normal real analytic

surfaces, J. reine angew. Math. 556 (2003) 99–111.

BOCHNAK J., COSTE M., ROY M.F., Real Algebraic Geometry, Ergeb. Math. Grenzgeb., vol. 36,Springer, Berlin, 1998.

CARTAN H., Variétés analytiques réelles et variétés analytiques complexes, Bull. Soc. Math. France 85 (1957)77–99.

CHOI M.D., DAI Z.D., LAM T.Y., REZNICK B., The Pythagoras number of some affine algebras and local algebras, J. reine angew. Math. 336 (1982) 45–82.

COEN S., Sul rango dei fasci coerenti, Boll. Univ. Mat. Ital. 22 (1967) 373–383.

GREENBERG M.J., Lectures on Forms in Many Variables, W.A. Benjamin, New York, 1969.

GUNNING R., ROSSI H., Analytic Functions of Several Complex Variables, Prentice-Hall, Englewood Cliffs, NJ, 1965.

JAWORSKI P., Positive definite analytic functions and vector bundles, Bull. Acad. Pol. Sci. 30 (1982)501–506.

JAWORSKI P., About estimates on number of squares necessary to represent a positive-semidefinite analytic function, Arch. Math. 58 (1992) 276–279.

DE JONG T., PFISTER G., Local Analytic Geometry, Basic Theory and Applications, Advanced Lectures in Mathematics, Vieweg, Braunschweig, 2000.

LAM T.Y., The Algebraic Theory of Quadratic Forms, Mathematics Lecture Notes Series, W.A.Benjamin, Massachusetts, 1973.

MAHÉ L., Level and Pythagoras number of some geometric rings, Math. Z. 204 (4) (1990) 615–629.

MAHÉ L., Théorème de Pfister pour les variétés et anneaux deWitt réduits, Invent. Math. 85 (1) (1986)53–72.

NARASIMHAN R., Introduction to the Theory of Analytic Spaces, Lecture Notes in Math., vol. 25,Springer, Berlin, 1966.

PFISTER A., Quadratic Forms with Applications to Algebraic Geometry and Topology, London Math.Soc. Lecture Note Ser., vol. 217, Cambridge University Press, Cambridge, 1995.

PRESTEL A., DELZELL C.N., Positive Polynomials, Monographs in Mathematics, Springer, Berlin,2001.

RUIZ J.M., The Basic Theory of Power Series, Advanced Lectures in Mathematics, Vieweg,Braunschweig, 1993.

TOUGERON J.-C., Idéaux de fonctions différentiables, Ergeb. Math. Grenzgeb., vol. 71, Springer,Berlin, 1972.

Deposited On:09 May 2012 09:52
Last Modified:06 Feb 2014 10:17

Repository Staff Only: item control page