No proper generalized quadratic forms are universal over quadratic fields
Fuente:
arXiv
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| Autori principali: | , , , , , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| Soggetti: | |
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| _version_ | 1866913498582220800 |
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| author | Chwiedziuk, Ondřej Doležálek, Matěj Hlavinková, Simona Pěchoučková, Emma Pezlar, Zdeněk Prakash, Om Růžičková, Anna Zindulka, Mikuláš |
| author_facet | Chwiedziuk, Ondřej Doležálek, Matěj Hlavinková, Simona Pěchoučková, Emma Pezlar, Zdeněk Prakash, Om Růžičková, Anna Zindulka, Mikuláš |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_07941 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | No proper generalized quadratic forms are universal over quadratic fields Chwiedziuk, Ondřej Doležálek, Matěj Hlavinková, Simona Pěchoučková, Emma Pezlar, Zdeněk Prakash, Om Růžičková, Anna Zindulka, Mikuláš Number Theory 11E12 (Primary), 11E20, 11E25, 11R11, 11R27, 11R80 (Secondary) 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. |
| title | No proper generalized quadratic forms are universal over quadratic fields |
| topic | Number Theory 11E12 (Primary), 11E20, 11E25, 11R11, 11R27, 11R80 (Secondary) |
| url | https://arxiv.org/abs/2409.07941 |