Sums of squares of linear forms
| dc.contributor.author | Fernando Galván, José Francisco | |
| dc.contributor.author | Ruiz Sancho, Jesús María | |
| dc.contributor.author | Scheiderer, Claus | |
| dc.date.accessioned | 2023-06-20T09:33:32Z | |
| dc.date.available | 2023-06-20T09:33:32Z | |
| dc.date.issued | 2006 | |
| dc.description.abstract | Let k be a real field. We show that every non-negative homogeneous quadratic polynomial f (x(1),..., x(n)) with coefficients in the polynomial ring k[t] is a sum of 2n center dot tau(k) squares of linear forms, where tau(k) is the supremum of the levels of the finite non-real field extensions of k. From this result we deduce bounds for the Pythagoras numbers of affine curves over fields, and of excellent two-dimensional local henselian rings. | |
| dc.description.department | Depto. de Álgebra, Geometría y Topología | |
| dc.description.faculty | Fac. de Ciencias Matemáticas | |
| dc.description.refereed | TRUE | |
| dc.description.status | pub | |
| dc.eprint.id | https://eprints.ucm.es/id/eprint/15130 | |
| dc.identifier.issn | 1073-2780 | |
| dc.identifier.officialurl | http://mrlonline.org/mrl/2006-013-006/2006-013-006-009.pdf | |
| dc.identifier.relatedurl | http://www.intlpress.com/ | |
| dc.identifier.uri | https://hdl.handle.net/20.500.14352/49900 | |
| dc.issue.number | 5-6 | |
| dc.journal.title | Mathematical Research Letters | |
| dc.language.iso | spa | |
| dc.page.final | 956 | |
| dc.page.initial | 947 | |
| dc.publisher | International Press | |
| dc.rights.accessRights | open access | |
| dc.subject.cdu | 511 | |
| dc.subject.cdu | 512.7 | |
| dc.subject.keyword | Sums of squares | |
| dc.subject.keyword | quadratic forms | |
| dc.subject.keyword | level | |
| dc.subject.keyword | Pythagoras numbers | |
| dc.subject.keyword | local henselian rings. | |
| 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 | Sums of squares of linear forms | |
| dc.type | journal article | |
| dc.volume.number | 13 | |
| dcterms.references | C. Andradas and J.M. Ruiz, On local uniformization of orderings, Contemp. Math. 155 (1994) 19–46. R. Baeza, D. Leep, M. O’Ryan, and J. P. Prieto, Sums of squares of linear forms, Math. Z. 193 (1986) 297–306. N. Bourbaki, Alg`ebre Commutative, Chapitres 8 et 9. Masson, Paris, 1983. M.D. Choi, Z.D. Dai, T.Y. Lam, and B. Reznick, The Pythagoras number of some affine algebras and local algebras, J. Reine Angew. Math. 336 (1982) 45–82. M.D. Choi, T.Y. Lam, and B. Reznick, Real zeros of positive semidefinite forms. I, Math. Z. 171 (1980) 1–26. D.ˇZ. Djokovi´c, Hermitian matrices over polynomial rings, J. Algebra 43 (1976) 359–374. J.F. Fernando, On the Pythagoras numbers of real analytic rings, J. Algebra 243 (2001) 321–338. Sums of squares in real analytic rings, Trans. Am. Math. Soc. 354 (2002) 1909– 1919. J.F. Fernando, J.M. Ruiz, and C. Scheiderer, Sums of squares in real rings, Trans. Am. Math. Soc. 356 (2004) 2663–2684. V.A. Jakubovi´c, Factorization of symmetric matrix polynomials (Russian), Dokl. Akad. Nauk SSSR 194 (1970) 532–535. M. Knebusch, Grothendieck- und Wittringe von nichtausgearteten symmetrischen Bilinearformen, S.-B. Heidelberger Akad. Wiss. Math.-Natur. Kl. 1969/70 93–157. H. Kurke, G. Pfister, D. Popescu, M. Roczen, and T. Mostowski, Die Approximationseigenschaft lokaler Ringe, Lecture Notes in Mathematics, Vol. 634. Springer-Verlag, Berlin-New York, 1978. T.Y. Lam, Introduction to quadratic forms over fields, Graduate Studies in Mathematics, 67. American Mathematical Society, Providence, RI, 2005. M. Rosenblum and J. Rovnyak, The factorization problem for nonnegative operator valued functions, Bull. Am. Math. Soc. 77 (1971) 287–318. W. Scharlau, Quadratic and Hermitian forms. Grundlehren der mathematischen Wissenschaften 270,Springer,Berlin,1985. C. Scheiderer, On sums of squares in local rings. J. Reine Angew. Math. 540 (2001) 205– 227. | |
| dspace.entity.type | Publication | |
| relation.isAuthorOfPublication | 499732d5-c130-4ea6-8541-c4ec934da408 | |
| relation.isAuthorOfPublication | f12f8d97-65c7-46aa-ad47-2b7099b37aa4 | |
| relation.isAuthorOfPublication.latestForDiscovery | 499732d5-c130-4ea6-8541-c4ec934da408 |
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