A uniform formula on the number of integer matrices with given determinant and height
Fuente:
arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866929711219736576 |
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| author | Afifurrahman, Muhammad |
| author_facet | Afifurrahman, Muhammad |
| contents | We obtain an asymptotic formula for the number of integer $2\times 2$ matrices that have determinant $Δ$ and whose absolute values of the entries are at most $H$. The result holds uniformly for a large range of $Δ$ with respect to $H$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_08191 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A uniform formula on the number of integer matrices with given determinant and height Afifurrahman, Muhammad Number Theory 11C20 (primary), 11D45, 11D72, 15B36 We obtain an asymptotic formula for the number of integer $2\times 2$ matrices that have determinant $Δ$ and whose absolute values of the entries are at most $H$. The result holds uniformly for a large range of $Δ$ with respect to $H$. |
| title | A uniform formula on the number of integer matrices with given determinant and height |
| topic | Number Theory 11C20 (primary), 11D45, 11D72, 15B36 |
| url | https://arxiv.org/abs/2407.08191 |