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arXiv · 2204.01997

On $n$-universal quadratic forms over dyadic local fields

Zilong He·Yong Hu
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Abstract

Let $ n \ge 2$ be an integer. We give necessary and sufficient conditions for an integral quadratic form over dyadic local fields to be $ n $-universal by using invariants from Beli's theory of bases of norm generators. Also, we provide a minimal set for testing $ n $-universal quadratic forms over dyadic local fields, as an analogue of Bhargava and Hanke's 290-theorem (or Conway and Schneeberger's 15-theorem) on universal quadratic forms with integer coefficients.

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Zilong He, Yong Hu. 2022-04-05. On $n$-universal quadratic forms over dyadic local fields. https://doi.org/10.1007/s11425-022-2133-0

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