Manin conjecture
if K-rational points on Fano variety are Zariski-dense subset, then the distribution of points of height: H(x)\leq B in any Zariski-open subset U is proportional to B \log (B)^{r-1}, where r is rank of Picard group of that variety.
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Source: List of unsolved problems in mathematics (CC BY-SA 4.0)