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On the pythagoras numbers of real analytic surfaces

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dc.contributor.authorAcquistapace, Francesca
dc.contributor.authorBroglia, Fabrizio
dc.contributor.authorFernando Galván, José Francisco
dc.contributor.authorRuiz Sancho, Jesús María
dc.date.accessioned2023-06-20T09:33:38Z
dc.date.available2023-06-20T09:33:38Z
dc.date.issued2005
dc.description.abstractWe 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.
dc.description.departmentDepto. de Álgebra, Geometría y Topología
dc.description.facultyFac. de Ciencias Matemáticas
dc.description.refereedTRUE
dc.description.sponsorshipRAAG
dc.description.sponsorshipGNSAGA
dc.description.sponsorshipINdAM
dc.description.sponsorshipMIUR
dc.description.sponsorshipGAAR
dc.description.statuspub
dc.eprint.idhttps://eprints.ucm.es/id/eprint/15149
dc.identifier.doi10.1016/j.ansens.2005.04.001
dc.identifier.issn0012-9593
dc.identifier.officialurlhttp://www.sciencedirect.com/science/article/pii/S0012959305000443
dc.identifier.relatedurlhttp://www.sciencedirect.com/
dc.identifier.urihttps://hdl.handle.net/20.500.14352/49905
dc.issue.number5
dc.journal.titleAnnales Scientifiques de l'École Normale Supérieure. Quatrième Série
dc.language.isoeng
dc.page.final772
dc.page.initial751
dc.publisherSociété Mathématique de France
dc.relation.projectIDHPRN-CT-2001-00271
dc.relation.projectIDBFM-2002-04797.
dc.rights.accessRightsrestricted access
dc.subject.cdu512.7
dc.subject.keywordPythagoras number
dc.subject.keywordAnalytic function
dc.subject.keywordAnalytic function germ
dc.subject.keywordMeromorphic function
dc.subject.keywordMeromorphic function germ
dc.subject.ucmGeometria algebraica
dc.subject.unesco1201.01 Geometría Algebraica
dc.titleOn the pythagoras numbers of real analytic surfaces
dc.typejournal article
dc.volume.number38
dcterms.referencesACQUISTAPACE 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.
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relation.isAuthorOfPublication.latestForDiscovery499732d5-c130-4ea6-8541-c4ec934da408

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