We adapt the approach of Rudnev, Shakan, and Shkredov (2018) to prove that in an arbitrary field , for all finite with if is positive, we have
This improves upon the exponent of given by an incidence theorem of Stevens and de Zeeuw.
"On products of shifts in arbitrary fields." Mosc. J. Comb. Number Theory 8 (3) 247 - 261, 2019. https://doi.org/10.2140/moscow.2019.8.247