No proper generalized quadratic forms are universal over quadratic fields

2024/09/12 by Ondřej Chwiedziuk, Chwiedziuk, Ondřej, Matěj Doležálek +13
Mathematics · #11E12 (Primary) #11E20 #11E25 #11R11 #11R27 #11R80 (Secondary) #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry and Number Theory #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2409.07941

openalex publication_date 2024/09/12 · openalex created_date 2024/10/23 · openalex updated_date 2026/07/28

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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