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arXiv · 2409.07941

No proper generalized quadratic forms are universal over quadratic fields

Ondřej Chwiedziuk·Matěj Doležálek·Simona Hlavinková·Emma Pěchoučková·Zdeněk Pezlar·Om Prakash·Anna Růžičková·Mikuláš Zindulka
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Abstract

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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Ondřej Chwiedziuk, Matěj Doležálek, Simona Hlavinková, Emma Pěchoučková, Zdeněk Pezlar, Om Prakash, Anna Růžičková, Mikuláš Zindulka. 2024-09-12. No proper generalized quadratic forms are universal over quadratic fields. https://arxiv.org/abs/2409.07941

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