no. 5
On the pythagoras numbers of real analytic surfaces
Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 38 (2005) no. 5, pp. 751-772. 
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     title = {On the pythagoras numbers of real analytic surfaces},
     journal = {Annales scientifiques de l'\'Ecole Normale Sup\'erieure},
     pages = {751--772},
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     volume = {Ser. 4, 38},
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Acquistapace, Francesca; Broglia, Fabrizio; Fernando, José F.; Ruiz, Jesús M. On the pythagoras numbers of real analytic surfaces. Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 38 (2005) no. 5, pp. 751-772. doi : 10.1016/j.ansens.2005.04.001. http://archive.numdam.org/articles/10.1016/j.ansens.2005.04.001/

[1] Acquistapace F., Broglia F., Fernando J.F., Ruiz J.M., On the 17th Hilbert Problem for global analytic functions, Preprint RAAG 2004.

[2] 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. | MR | Zbl

[3] Bochnak J., Coste M., Roy M.F., Real Algebraic Geometry, Ergeb. Math. Grenzgeb., vol. 36, Springer, Berlin, 1998. | MR | Zbl

[4] Cartan H., Variétés analytiques réelles et variétés analytiques complexes, Bull. Soc. Math. France 85 (1957) 77-99. | Numdam | MR | Zbl

[5] 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. | MR | Zbl

[6] Coen S., Sul rango dei fasci coerenti, Boll. Univ. Mat. Ital. 22 (1967) 373-383. | MR | Zbl

[7] Greenberg M.J., Lectures on Forms in Many Variables, W.A. Benjamin, New York, 1969. | MR | Zbl

[8] Gunning R., Rossi H., Analytic Functions of Several Complex Variables, Prentice-Hall, Englewood Cliffs, NJ, 1965. | MR | Zbl

[9] Jaworski P., Positive definite analytic functions and vector bundles, Bull. Acad. Pol. Sci. 30 (1982) 501-506. | MR | Zbl

[10] Jaworski P., About estimates on number of squares necessary to represent a positive-semidefinite analytic function, Arch. Math. 58 (1992) 276-279. | MR | Zbl

[11] De Jong T., Pfister G., Local Analytic Geometry, Basic Theory and Applications, Advanced Lectures in Mathematics, Vieweg, Braunschweig, 2000. | MR | Zbl

[12] Lam T.Y., The Algebraic Theory of Quadratic Forms, Mathematics Lecture Notes Series, W.A. Benjamin, Massachusetts, 1973. | MR | Zbl

[13] Mahé L., Level and Pythagoras number of some geometric rings, Math. Z. 204 (4) (1990) 615-629. | MR | Zbl

[14] Mahé L., Théorème de Pfister pour les variétés et anneaux de Witt réduits, Invent. Math. 85 (1) (1986) 53-72. | MR | Zbl

[15] Narasimhan R., Introduction to the Theory of Analytic Spaces, Lecture Notes in Math., vol. 25, Springer, Berlin, 1966. | MR | Zbl

[16] Pfister A., Quadratic Forms with Applications to Algebraic Geometry and Topology, London Math. Soc. Lecture Note Ser., vol. 217, Cambridge University Press, Cambridge, 1995. | MR | Zbl

[17] Prestel A., Delzell C.N., Positive Polynomials, Monographs in Mathematics, Springer, Berlin, 2001. | MR | Zbl

[18] Ruiz J.M., The Basic Theory of Power Series, Advanced Lectures in Mathematics, Vieweg, Braunschweig, 1993. | MR

[19] Tougeron J.-C., Idéaux de fonctions différentiables, Ergeb. Math. Grenzgeb., vol. 71, Springer, Berlin, 1972. | MR | Zbl

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