Kitaoka's conjecture and sums of squares

2026/07/20 by Vítězslav Kala, Kristýna Kramer, Katharina Kramer +1
Mathematics · #Analytic Number Theory Research #Algebraic Geometry and Number Theory #Advanced Algebra and Geometry

paper · doi:10.1112/blms.70445

Abstract

Abstract 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 squares (if does not contain 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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