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| Format: | Preprint |
| Veröffentlicht: |
2024
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| Schlagworte: | |
| Online-Zugang: | https://arxiv.org/abs/2408.03774 |
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| _version_ | 1866913460590215168 |
|---|---|
| author | Diao, Yijie |
| author_facet | Diao, Yijie |
| contents | We provide an estimate for the number of nontrivial integer points on the Pellian surface $t^2 - du^2 = 1$ in a bounded region. We give a lower bound on the size of fundamental solutions for almost all $d$ in a certain class, based on a recent conjecture of Browning and Wilsch about integer points on log K3 surfaces. We also obtain an upper bound on the average of class number in this class, assuming the same conjecture. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_03774 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Class numbers and integer points on some Pellian surfaces Diao, Yijie Number Theory 11D25 (11N56) We provide an estimate for the number of nontrivial integer points on the Pellian surface $t^2 - du^2 = 1$ in a bounded region. We give a lower bound on the size of fundamental solutions for almost all $d$ in a certain class, based on a recent conjecture of Browning and Wilsch about integer points on log K3 surfaces. We also obtain an upper bound on the average of class number in this class, assuming the same conjecture. |
| title | Class numbers and integer points on some Pellian surfaces |
| topic | Number Theory 11D25 (11N56) |
| url | https://arxiv.org/abs/2408.03774 |