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Kitaoka's Conjecture for quadratic fields

· 2025 · math.NT · arXiv 2501.19371

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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.

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math.NT 1

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2026 1

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CONDITIONAL 1

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Escalations and criteria over real quadratic fields

math.NT · 2026-08-12 · conditional · novelty 7.0

The authors generalize the escalation method to number fields, prove finiteness of criterion sets, and compute, conjecturally and in one case exactly, the analogue of the 15-Theorem over Q(√2), Q(√3), and Q(√5).

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  • Escalations and criteria over real quadratic fields math.NT · 2026-08-12 · conditional · none · ref 39 · internal anchor

    The authors generalize the escalation method to number fields, prove finiteness of criterion sets, and compute, conjecturally and in one case exactly, the analogue of the 15-Theorem over Q(√2), Q(√3), and Q(√5).