Abstract

We adapt the approach of Rudnev, Shakan, and Shkredov (2018) to prove that in an arbitrary field $\mathbb{F}$, for all $A\subset \mathbb{F}$ finite with $\left|A\right|<p^{1∕4}$ if $p:=Char\left(\mathbb{F}\right)$ is positive, we have

This improves upon the exponent of $\frac{6}{5}$ given by an incidence theorem of Stevens and de Zeeuw.

Keywords

Mathematical Subject Classification 2010

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