36 citations · 235 across the 39 of their papers we have counts for
6 papers · 1 filter
Universality criterion sets for quadratic forms over number fields
Vitezslav Kala, Jakub Krásenský, Giuliano Romeo
In analogy with the 290-Theorem of Bhargava-Hanke, a criterion set is a finite subset of the totally positive integers in a given totally real number field such that if a quadr…
Most totally real fields do not have universal forms or Northcott property
Nicolas Daans, Vitezslav Kala, Siu Hang Man +2
We show that, in the space of all totally real fields equipped with the constructible topology, the set of fields that admit a universal quadratic form, or have the Northcott prope…
Universality lifting from a general base field
Vitezslav Kala, Daejun Kim, Seok Hyeong Lee
Given a totally real number field , we show that there are only finitely many totally real extensions of of a fixed degree that admit a universal quadratic form defined over…
There is no 290-Theorem for higher degree forms
Vitezslav Kala, Om Prakash
We study the universality of forms of degrees greater than 2 over rings of integers of totally real number fields. We show that such universal forms always exist, but cannot be cha…
Sails for universal quadratic forms
Vítězslav Kala, Siu Hang Man
We establish a new connection between sails, a key notion in the geometric theory of generalised continued fractions, and arithmetic of totally real number fields, specifically, un…
Even better sums of squares over quintic and cyclotomic fields
Vitezslav Kala, Pavlo Yatsyna
We classify all totally real number fields of degree at most 5 that admit a universal quadratic form with rational integer coefficients; in fact, there are none over the previously…