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Kitaoka's Conjecture and sums of squares

Published 22 Oct 2025 in math.NT | (2510.19545v1)

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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