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arxiv: 1801.00979 · v3 · pith:POD72RJ2new · submitted 2018-01-03 · 🧮 math.NT

Counting rational points on quadric surfaces

classification 🧮 math.NT
keywords boundoptimalpointsrationalcountingdefineddependenceexplicit
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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 $Q$.

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