Kitaoka's Conjecture for quadratic fields
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arXiv
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| Main Authors: | , , , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866912213243002880 |
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| author | Kala, Vitezslav Krásenský, Jakub Park, Dayoon Yatsyna, Pavlo Żmija, Błażej |
| author_facet | Kala, Vitezslav Krásenský, Jakub Park, Dayoon Yatsyna, Pavlo Żmija, Błażej |
| contents | We prove that there are at most 13 real quadratic fields that admit a ternary universal quadratic lattice, thus establishing a strong version of Kitaoka's Conjecture for quadratic fields. More generally, we obtain explicit upper bounds on the discriminants of real quadratic fields with a quadratic lattice of rank at most 7 that represents all totally positive multiples of a fixed integer. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_19371 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Kitaoka's Conjecture for quadratic fields Kala, Vitezslav Krásenský, Jakub Park, Dayoon Yatsyna, Pavlo Żmija, Błażej Number Theory 11E12, 11E20, 11E25, 11R04, 11R11, 11R80 We prove that there are at most 13 real quadratic fields that admit a ternary universal quadratic lattice, thus establishing a strong version of Kitaoka's Conjecture for quadratic fields. More generally, we obtain explicit upper bounds on the discriminants of real quadratic fields with a quadratic lattice of rank at most 7 that represents all totally positive multiples of a fixed integer. |
| title | Kitaoka's Conjecture for quadratic fields |
| topic | Number Theory 11E12, 11E20, 11E25, 11R04, 11R11, 11R80 |
| url | https://arxiv.org/abs/2501.19371 |