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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)d1, 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 language  English 

Pages (fromto)  854864 
Number of pages  11 
Journal  Bulletin of the London Mathematical Society 
Volume  55 
Issue number  2 
Early online date  7 Dec 2022 
DOIs  
Publication status  Published  Apr 2023 
MoE publication type  A1 Journal articlerefereed 
Keywords
 TOTALLY POSITIVE NUMBERS
 LATTICES
 RANK
 ORDERS
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Hollanti NT: Numbertheoretic wellrounded lattices
Hollanti, C., Miller, N., Bolanos Chavez, W., Matalaaho, T. & Vieira Lino Da Costa, M.
01/09/2022 → 31/08/2026
Project: Academy of Finland: Other research funding

Hollanti_ICT: Secure Distributed Computation Schemes with Applications to Digitalized Remote Healthcare
Hollanti, C., Villamizar Rubiano, D., Hietaaho, E., Sacikara Kariksiz, E., Yatsyna, P., Kas Hanna, S., Makkonen, O., Matalaaho, T., Karpuk, D., Bolanos Chavez, W. & Allaix, M.
01/01/2021 → 31/12/2023
Project: Academy of Finland: Other research funding