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Kitaoka's Conjecture and sums of squares
[Submitted on 22 Oct 2025 (v1), last revised 17 Jun 2026 (this v · 2026-06-18 · via math updates on arXiv.org

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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.

Submission history

From: Kristýna Kramer [view email]
[v1] Wed, 22 Oct 2025 12:52:03 UTC (24 KB)
[v2] Wed, 17 Jun 2026 12:05:40 UTC (25 KB)