On the Pythagoras numbers of real analytic curves.
| dc.contributor.author | Acquistapace, Francesca | |
| dc.contributor.author | Broglia, Fabrizio | |
| dc.contributor.author | Ruiz Sancho, Jesús María | |
| dc.date.accessioned | 2023-06-20T09:33:31Z | |
| dc.date.available | 2023-06-20T09:33:31Z | |
| dc.date.issued | 2007 | |
| dc.description.abstract | We show that the Pythagoras number of a real analytic curve is the supremum of the Pythagoras numbers of its singularities, or that supremum plus 1. This includes cases when the Pythagoras number is infinite. | |
| dc.description.department | Depto. de Álgebra, Geometría y Topología | |
| dc.description.faculty | Fac. de Ciencias Matemáticas | |
| dc.description.refereed | TRUE | |
| dc.description.sponsorship | GNSAGA | |
| dc.description.sponsorship | INdAM | |
| dc.description.sponsorship | MIUR | |
| dc.description.sponsorship | GEOR | |
| dc.description.sponsorship | UCM | |
| dc.description.status | pub | |
| dc.eprint.id | https://eprints.ucm.es/id/eprint/15127 | |
| dc.identifier.doi | 10.1007/s00209-007-0107-6 | |
| dc.identifier.issn | 0025-5874 | |
| dc.identifier.officialurl | http://www.springerlink.com/content/v7545081u3w74649/fulltext.pdf | |
| dc.identifier.relatedurl | http://www.springerlink.com/ | |
| dc.identifier.uri | https://hdl.handle.net/20.500.14352/49899 | |
| dc.issue.number | 1 | |
| dc.journal.title | Mathematische Zeitschrift | |
| dc.language.iso | eng | |
| dc.page.final | 21 | |
| dc.page.initial | 13 | |
| dc.publisher | Springer | |
| dc.relation.projectID | MTM2005-02865 | |
| dc.relation.projectID | 910444. | |
| dc.rights.accessRights | restricted access | |
| dc.subject.cdu | 512.7 | |
| dc.subject.cdu | 511 | |
| dc.subject.keyword | Pythagoras number | |
| dc.subject.keyword | Sum of squares | |
| dc.subject.keyword | Analytic curve Germ | |
| dc.subject.keyword | Global analytic curve | |
| dc.subject.ucm | Teoría de números | |
| dc.subject.ucm | Geometria algebraica | |
| dc.subject.unesco | 1205 Teoría de Números | |
| dc.subject.unesco | 1201.01 Geometría Algebraica | |
| dc.title | On the Pythagoras numbers of real analytic curves. | |
| dc.type | journal article | |
| dc.volume.number | 257 | |
| dcterms.references | Bochnak, J., Risler, J.-J.: Le théorème des zéros pour les variétés analytiques réelles de dimension 2. Ann. Sci. Écol. Norm. Sup. Paris 8, 353–364 (1975) Campillo, A., Ruiz, J.M.: Some remarks on pythagorean real curve germs. J. Algebra 128,271–275 (1990) 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, 45–82 (1982) Coen, S.: Sul rango dei fasci coerenti. Boll. UMI. 22, 373–383 (1967) Fernando, J.F., Quarez, R.: A remark on the Pythagoras number of algebroid curves. J. Algebra 274, 64–67 (2004) Fernando, J.F., Ruiz, J.M.: On the Pythagoras numbers of real analytic set germs. Bull. Soc.Math.France 133, 349–362 (2005) Fernando, J.F., Ruiz, J.M., Scheiderer, C.: Sums of squares in real rings. Trans. Am. Math.Soc. 356, 2663–2684 (2004) Jaworski, P.: Positive definite analytic functions and vector bundles. Bull. Acad. Polon. Sci. 30,501–506 (1982) Ortega, J.: On the Pythagoras number of a real irreducible algebroid curve. Math. Ann. 289,111–123 (1991) Quarez, R.: Pythagoras numbers of real algebroid curves and Gram matrices. J. Algebra 238,139–158 (2001) Ruiz, J.M.: On Hilbert’s 17th problem and real Nullstellensatz for global analytic functions.Math Z. 190, 447–459 (1985) Scheiderer, C.: Sums of squares of regular functions on real algebraic varieties. Trans. Am. Math.Soc. 352, 1039–1069 (1999) Scheiderer, C.: On sums of squares in local rings. J. Reine Angew. Math. 540, 205–227 (2001) | |
| dspace.entity.type | Publication | |
| relation.isAuthorOfPublication | f12f8d97-65c7-46aa-ad47-2b7099b37aa4 | |
| relation.isAuthorOfPublication.latestForDiscovery | f12f8d97-65c7-46aa-ad47-2b7099b37aa4 |
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