Counting rational points on quadric surfaces
We give an upper bound for the number of rational points of height at most B, lying on a surface defined by a quadratic form Q. The bound shows an explicit dependence on Q. It is optimal with respect to B, and is also optimal for typical forms Q.
| Main Authors: | , |
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| Format: | Journal article |
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Discrete Analysis
2018
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| _version_ | 1826256988835676160 |
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| author | Browning, T Heath-Brown, D |
| author_facet | Browning, T Heath-Brown, D |
| author_sort | Browning, T |
| collection | OXFORD |
| description | We give an upper bound for the number of rational points of height at most B, lying on a surface defined by a quadratic form Q. The bound shows an explicit dependence on Q. It is optimal with respect to B, and is also optimal for typical forms Q. |
| first_indexed | 2024-03-06T18:11:01Z |
| format | Journal article |
| id | oxford-uuid:03061062-7423-43da-9920-3ce96b3a1c8e |
| institution | University of Oxford |
| last_indexed | 2024-03-06T18:11:01Z |
| publishDate | 2018 |
| publisher | Discrete Analysis |
| record_format | dspace |
| spelling | oxford-uuid:03061062-7423-43da-9920-3ce96b3a1c8e2022-03-26T08:43:52ZCounting rational points on quadric surfacesJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:03061062-7423-43da-9920-3ce96b3a1c8eSymplectic Elements at OxfordDiscrete Analysis2018Browning, THeath-Brown, DWe give an upper bound for the number of rational points of height at most B, lying on a surface defined by a quadratic form Q. The bound shows an explicit dependence on Q. It is optimal with respect to B, and is also optimal for typical forms Q. |
| spellingShingle | Browning, T Heath-Brown, D Counting rational points on quadric surfaces |
| title | Counting rational points on quadric surfaces |
| title_full | Counting rational points on quadric surfaces |
| title_fullStr | Counting rational points on quadric surfaces |
| title_full_unstemmed | Counting rational points on quadric surfaces |
| title_short | Counting rational points on quadric surfaces |
| title_sort | counting rational points on quadric surfaces |
| work_keys_str_mv | AT browningt countingrationalpointsonquadricsurfaces AT heathbrownd countingrationalpointsonquadricsurfaces |