Kitaoka's Conjecture for quadratic fields

2025/01/31 by Kala, Vitezslav, Krásenský, Jakub, Park, Dayoon +2 · 2 citations
#11E12 #11E20 #11E25 #11R04 #11R11 #11R80 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2501.19371

Abstract

We prove that there are at most 13 real quadratic fields that admit a ternary universal quadratic lattice, thus establishing a strong version of Kitaoka's Conjecture for quadratic fields. More generally, we obtain explicit upper bounds on the discriminants of real quadratic fields with a quadratic lattice of rank at most 7 that represents all totally positive multiples of a fixed integer.

Cited by

• Asymptotics of n-universal lattices over number fields
• Kitaoka's Conjecture and sums of squares

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