On Kitaoka's conjecture and lifting problem for universal quadratic forms

dc.contributorAalto-yliopistofi
dc.contributorAalto Universityen
dc.contributor.authorKala, Vitezslaven_US
dc.contributor.authorYatsyna, Pavloen_US
dc.contributor.departmentDepartment of Mathematics and Systems Analysisen
dc.contributor.groupauthorAlgebra and Discrete Mathematicsen
dc.contributor.organizationCharles Universityen_US
dc.date.accessioned2023-08-23T06:07:42Z
dc.date.available2023-08-23T06:07:42Z
dc.date.issued2023-04en_US
dc.description.abstractFor 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.versionPeer revieweden
dc.format.extent11
dc.format.extent854-864
dc.format.mimetypeapplication/pdfen_US
dc.identifier.citationKala, 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.12762en
dc.identifier.doi10.1112/blms.12762en_US
dc.identifier.issn0024-6093
dc.identifier.otherPURE UUID: 5ec6985d-1c87-44d8-ac08-43d3dce1b6f6en_US
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dc.identifier.otherPURE FILEURL: https://research.aalto.fi/files/118849906/SCI_Kala_etal_Bulletin_of_the_London_Mathematical_Society_2023.pdfen_US
dc.identifier.urihttps://aaltodoc.aalto.fi/handle/123456789/122639
dc.identifier.urnURN:NBN:fi:aalto-202308234985
dc.language.isoenen
dc.publisherOxford University Press
dc.relation.ispartofseriesBULLETIN OF THE LONDON MATHEMATICAL SOCIETYen
dc.relation.ispartofseriesVolume 55, issue 2en
dc.rightsopenAccessen
dc.subject.keywordTOTALLY POSITIVE NUMBERSen_US
dc.subject.keywordLATTICESen_US
dc.subject.keywordRANKen_US
dc.subject.keywordORDERSen_US
dc.titleOn Kitaoka's conjecture and lifting problem for universal quadratic formsen
dc.typeA1 Alkuperäisartikkeli tieteellisessä aikakauslehdessäfi
dc.type.versionacceptedVersion
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