Vítězslav Kala

activity

20092026

most citedNumber fields without n-ary universal quadratic forms

36 citations · 235 across the 39 of their papers we have counts for

collaborators

Showing 2021Show all

3 papers · 1 filter

math.NT2021★ 9 cited

Consecutive real quadratic fields with large class numbers

Giacomo Cherubini, Alessandro Fazzari, Andrew Granville +2

For a given positive integer $k$ , we prove that there are at least $x^{1/2 - o (1)}$ integers $d \leq x$ such that the real quadratic fields $\mathbb Q(\sqrt{d+1}),\dots,\mathbb Q(\sqr…

math.NT2021★ 19 cited

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

Vítězslav Kala, Pavlo Yatsyna

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…

math.NT2021★ 13 cited

Number fields without universal quadratic forms of small rank exist in most degrees

Vítězslav Kala

We prove that in each degree divisible by 2 or 3, there are infinitely many totally real number fields that require universal quadratic forms to have arbitrarily large rank.