On the finiteness of Pythagoras numbers of real meromorphic functions.
| dc.contributor.author | Acquistapace, Francesca | |
| dc.contributor.author | Broglia, Fabrizio | |
| dc.contributor.author | Fernando Galván, José Francisco | |
| dc.contributor.author | Ruiz Sancho, Jesús María | |
| dc.date.accessioned | 2023-06-20T00:11:27Z | |
| dc.date.available | 2023-06-20T00:11:27Z | |
| dc.date.issued | 2010 | |
| dc.description.abstract | We consider the 17(th) Hilbert Problem for global real analytic functions in a modified form that involves infinite sums of squares. Then we prove a local-global principle for a real global analytic function to be a sum of squares of global real meromorphic functions. We deduce that an affirmative solution to the 17(th) Hilbert Problem for global real analytic functions implies the finiteness of the Pythagoras number of the field of global real meromorphic functions, hence that of the field of real meromorphic power series. This measures the difficulty of the 17(th) Hilbert problem in the analytic case. | |
| dc.description.department | Depto. de Álgebra, Geometría y Topología | |
| dc.description.faculty | Fac. de Ciencias Matemáticas | |
| dc.description.refereed | TRUE | |
| dc.description.sponsorship | Italian GNSAGA | |
| dc.description.sponsorship | INdAM | |
| dc.description.sponsorship | MIUR | |
| dc.description.sponsorship | Spanish GEOR | |
| dc.description.status | pub | |
| dc.eprint.id | https://eprints.ucm.es/id/eprint/15094 | |
| dc.identifier.issn | 0037-9484 | |
| dc.identifier.officialurl | http://cat.inist.fr/?aModele=afficheN&cpsidt=22896755 | |
| dc.identifier.uri | https://hdl.handle.net/20.500.14352/42160 | |
| dc.issue.number | 2 | |
| dc.journal.title | Bulletin de la Société Mathématique de France | |
| dc.page.final | 247 | |
| dc.page.initial | 231 | |
| dc.publisher | French Mathematical Society | |
| dc.relation.projectID | MTM-2005-02865 | |
| dc.rights.accessRights | metadata only access | |
| dc.subject.cdu | 512.7 | |
| dc.subject.keyword | 17th Hilbert problem | |
| dc.subject.keyword | Pythagoras number | |
| dc.subject.keyword | Sum of squares | |
| dc.subject.keyword | Bad set | |
| dc.subject.keyword | Germs | |
| dc.subject.ucm | Geometria algebraica | |
| dc.subject.unesco | 1201.01 Geometría Algebraica | |
| dc.title | On the finiteness of Pythagoras numbers of real meromorphic functions. | |
| dc.type | journal article | |
| dc.volume.number | 138 | |
| 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 |