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- W1662008081 abstract "This note is based on an application of the plane-point incidence theorem in the projective space $FP^3$, where $F$ is a field of characteristics $p>2$. It shows that a Cartesian product point set $P=Atimes Ain F^2$, with $|A|leq p^{2/3}$ determines $Omega(|P|^{3/4})$ distinct directions, $O(|P|^{9/4})$ collinear point triples and $Omega(|P|^{3/2})$ distinct lines in $F^2$. The argument also yields sum-product type inequalities, e.g. $|(A-A)(A-A) | gg |A|^{3/2},$ which are reasonably strong when $A$ has small additive doubling." @default.
- W1662008081 created "2016-06-24" @default.
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- W1662008081 date "2015-08-20" @default.
- W1662008081 modified "2023-09-27" @default.
- W1662008081 title "Some new sum-product type inequalities in positive characteristic" @default.
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