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

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اقرأ أكثر حفظ في قائمتي
  • معلومة اضافية
    • Contributors:
      Department of Mathematics and Systems Analysis; Algebra and Discrete Mathematics; Charles University; Aalto-yliopisto; Aalto University
    • بيانات النشر:
      Oxford University Press
    • الموضوع:
      2023
    • Collection:
      Aalto University Publication Archive (Aaltodoc) / Aalto-yliopiston julkaisuarkistoa
    • نبذة مختصرة :
      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. ; Peer reviewed
    • File Description:
      854-864; application/pdf
    • ISSN:
      0024-6093
    • Relation:
      BULLETIN OF THE LONDON MATHEMATICAL SOCIETY; Volume 55, issue 2; 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; PURE UUID: 5ec6985d-1c87-44d8-ac08-43d3dce1b6f6; PURE ITEMURL: https://research.aalto.fi/en/publications/5ec6985d-1c87-44d8-ac08-43d3dce1b6f6; PURE LINK: http://www.scopus.com/inward/record.url?scp=85144767441&partnerID=8YFLogxK; PURE FILEURL: https://research.aalto.fi/files/118849906/SCI_Kala_etal_Bulletin_of_the_London_Mathematical_Society_2023.pdf; https://aaltodoc.aalto.fi/handle/123456789/122639; URN:NBN:fi:aalto-202308234985
    • الرقم المعرف:
      10.1112/blms.12762
    • Rights:
      openAccess
    • الرقم المعرف:
      edsbas.FC1A5CB0