Counting rational points on quadric surfaces
Abstract
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 $Q$.
- Publication:
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arXiv e-prints
- Pub Date:
- January 2018
- DOI:
- 10.48550/arXiv.1801.00979
- arXiv:
- arXiv:1801.00979
- Bibcode:
- 2018arXiv180100979B
- Keywords:
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- Mathematics - Number Theory
- E-Print:
- 29 pages