Collinear triples and quadruples for Cartesian products in ${\mathbb{F}}_p^2$

Abstract

In this ote, which has been absorbed by arXiv1702.01003, we combine a recent point-line incidence bound of Stevens and de Zeeuw with an older lemma of Bourgain, Katz and Tao to bound the number of collinear triples and quadruples in a Cartesian product in ${\mathbb{F}}_p^2$.

10 pages

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• Any small multiplicative sugroup is not a sumset