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<p>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.</p>

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No proper generalized quadratic forms are universal over quadratic fields

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年3月21日

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  • Ondřej Chwiedziuk,
  • Matěj Doležálek,
  • Simona Fryšová,
  • Emma Pěchoučková,
  • Zdeněk Pezlar,
  • Om Prakash,
  • Anna Růžičková,
  • Mikuláš Zindulka

摘要

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.