没有适当的广义二次型是在二次域上通用的

arXiv - MATH - Number Theory Pub Date : 2024-09-12 DOI:arxiv-2409.07941

Ondřej ChwiedziukCharles University, Matěj DoležálekCharles University, Simona HlavinkováCharles University, Emma PěchoučkováCharles University, Zdeněk PezlarCharles University, Om PrakashCharles University, Anna RůžičkováCharles University, Mikuláš ZindulkaCharles University

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摘要

我们考虑了实二次数域上的广义二次型，并在一个自然的正定义条件下证明，广义二次型只有包含一个广义二次型子形式，才可能是广义二次型。我们还构造了一个例子，说明正定义条件是必要的。

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No proper generalized quadratic forms are universal over quadratic fields

We consider generalized quadratic forms over real quadratic number fields and prove, under a natural positive-definiteness condition, that a generalized quadratic form can only be universal if it contains a quadratic subform that is universal. We also construct an example illustrating that the positive-definiteness condition is necessary.

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arXiv - MATH - Number Theory

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