No proper generalized quadratic forms are universal over quadratic fields
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.
Authors
- Matěj Doležálek (ORCID: https://orcid.org/0000-0002-2128-1601)
- Anna Růžičková
- Mikuláš Zindulka (ORCID: https://orcid.org/0009-0005-5862-3125)
- Zdeněk Pezlar
- Om Prakash (ORCID: https://orcid.org/0009-0007-2124-9736)
- Ondřej Chwiedziuk
- Simona Fryšová
- Emma Pěchoučková
Institutions
- Charles University (CZ)
Publication Details
- Journal
- The Ramanujan Journal
- Published
- 2026-03-21
- DOI
- https://doi.org/10.1007/s11139-026-01370-0
- Primary Topic
- Algebraic Geometry and Number Theory
- Type
- article
- Field-Weighted Citation Impact
- 0.00