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

Vitezslav Kala*, Pavlo Yatsyna

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

3 Citations (Scopus)
18 Downloads (Pure)

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.

Original languageEnglish
Pages (from-to)854-864
Number of pages11
JournalBulletin of the London Mathematical Society
Volume55
Issue number2
Early online date7 Dec 2022
DOIs
Publication statusPublished - Apr 2023
MoE publication typeA1 Journal article-refereed

Keywords

  • TOTALLY POSITIVE NUMBERS
  • LATTICES
  • RANK
  • ORDERS

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