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math.NT2026
Non-universality of ternary quadratic forms over fields containing
Kristyna Kramer, Jakub Krasensky
We prove Kitaoka's conjecture for all totally real number fields of degree 4 -- namely, there is no positive definite classical quadratic form in three variables which is universal…
math.NT2025
Kitaoka's Conjecture and sums of squares
Vitezslav Kala, Kristyna Kramer, Jakub Krasensky
We connect the existence of a ternary classical universal quadratic form over a totally real number field with the property that all totally positive multiples of 2 are sums of…