On Kitaoka's conjecture and lifting problem for universal quadratic forms
dc.contributor | Aalto-yliopisto | fi |
dc.contributor | Aalto University | en |
dc.contributor.author | Kala, Vitezslav | en_US |
dc.contributor.author | Yatsyna, Pavlo | en_US |
dc.contributor.department | Department of Mathematics and Systems Analysis | en |
dc.contributor.groupauthor | Algebra and Discrete Mathematics | en |
dc.contributor.organization | Charles University | en_US |
dc.date.accessioned | 2023-08-23T06:07:42Z | |
dc.date.available | 2023-08-23T06:07:42Z | |
dc.date.issued | 2023-04 | en_US |
dc.description.abstract | For a totally positive definite quadratic form over the ring of integers of a totally real number field K, we show that there are only finitely many totally real field extensions of K of a fixed degree over which the form is universal (namely, those that have a short basis in a suitable sense). Along the way we give a general construction of a universal form of rank bounded by D(logD)d-1, where d is the degree of K over Q and D is its discriminant. Furthermore, for any fixed degree we prove (weak) Kitaoka's conjecture that there are only finitely many totally real number fields with a universal ternary quadratic form. | en |
dc.description.version | Peer reviewed | en |
dc.format.extent | 11 | |
dc.format.extent | 854-864 | |
dc.format.mimetype | application/pdf | en_US |
dc.identifier.citation | Kala, V & Yatsyna, P 2023, ' On Kitaoka's conjecture and lifting problem for universal quadratic forms ', Bulletin of the London Mathematical Society, vol. 55, no. 2, pp. 854-864 . https://doi.org/10.1112/blms.12762 | en |
dc.identifier.doi | 10.1112/blms.12762 | en_US |
dc.identifier.issn | 0024-6093 | |
dc.identifier.other | PURE UUID: 5ec6985d-1c87-44d8-ac08-43d3dce1b6f6 | en_US |
dc.identifier.other | PURE ITEMURL: https://research.aalto.fi/en/publications/5ec6985d-1c87-44d8-ac08-43d3dce1b6f6 | en_US |
dc.identifier.other | PURE LINK: http://www.scopus.com/inward/record.url?scp=85144767441&partnerID=8YFLogxK | en_US |
dc.identifier.other | PURE FILEURL: https://research.aalto.fi/files/118849906/SCI_Kala_etal_Bulletin_of_the_London_Mathematical_Society_2023.pdf | en_US |
dc.identifier.uri | https://aaltodoc.aalto.fi/handle/123456789/122639 | |
dc.identifier.urn | URN:NBN:fi:aalto-202308234985 | |
dc.language.iso | en | en |
dc.publisher | Oxford University Press | |
dc.relation.ispartofseries | BULLETIN OF THE LONDON MATHEMATICAL SOCIETY | en |
dc.relation.ispartofseries | Volume 55, issue 2 | en |
dc.rights | openAccess | en |
dc.subject.keyword | TOTALLY POSITIVE NUMBERS | en_US |
dc.subject.keyword | LATTICES | en_US |
dc.subject.keyword | RANK | en_US |
dc.subject.keyword | ORDERS | en_US |
dc.title | On Kitaoka's conjecture and lifting problem for universal quadratic forms | en |
dc.type | A1 Alkuperäisartikkeli tieteellisessä aikakauslehdessä | fi |
dc.type.version | acceptedVersion |