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arXiv · 2510.19545

Kitaoka's Conjecture and sums of squares

Vitezslav Kala·Kristyna Kramer·Jakub Krasensky
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Abstract

We connect the existence of a ternary classical universal quadratic form over a totally real number field $K$ with the property that all totally positive multiples of 2 are sums of squares (if $K$ does not contain $\sqrt 2$ or contains a nonsquare totally positive unit). In particular, we get that Kitaoka's Conjecture holds for all fields of odd discriminant.

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Vitezslav Kala, Kristyna Kramer, Jakub Krasensky. 2025-10-22. Kitaoka's Conjecture and sums of squares. https://doi.org/10.1112/blms.70445

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