Using continued fractions with prescribed period for universal quadratic forms
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866912823991336960 |
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| author | Mensikova, Veronika Muchova, Helena |
| author_facet | Mensikova, Veronika Muchova, Helena |
| contents | We study the congruence classes attained by positive integers $D$ with a prescribed period of the continued fraction of $\sqrt D$. As an application, we refine the available results on large ranks of universal quadratic forms over real quadratic fields by also imposing congruence conditions on their discriminants. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_09419 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Using continued fractions with prescribed period for universal quadratic forms Mensikova, Veronika Muchova, Helena Number Theory 11A55, 11E12, 11R11 We study the congruence classes attained by positive integers $D$ with a prescribed period of the continued fraction of $\sqrt D$. As an application, we refine the available results on large ranks of universal quadratic forms over real quadratic fields by also imposing congruence conditions on their discriminants. |
| title | Using continued fractions with prescribed period for universal quadratic forms |
| topic | Number Theory 11A55, 11E12, 11R11 |
| url | https://arxiv.org/abs/2601.09419 |