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math.NT2024
Failures of integral Springer's Theorem
Nicolas Daans, Vítězslav Kala, Jakub Krásenský +1
We discuss the phenomenon where an element in a number field is not integrally represented by a given positive definite quadratic form, but becomes integrally represented by this f…
math.NT2018★ 33 cited
Lifting problem for universal quadratic forms
Vítězslav Kala, Pavlo Yatsyna
We study totally real number fields that admit a universal quadratic form whose coefficients are rational integers. We show that is the only such real quadrati…
math.NT2017
On the rank of universal quadratic forms over real quadratic fields
Valentin Blomer, Vítězslav Kala
We study the minimal number of variables required by a totally positive definite diagonal universal quadratic form over a real quadratic field and obtain lower…