In this paper, we study the Erdős distinct distances problem for Cartesian product sets in the setting of arbitrary finite fields. More precisely, let be an arbitrary finite field and be a set in . Suppose for any subfield and , then Using the same method, we also obtain some results on sum–product type problems.
"Distance sets over arbitrary finite fields." Illinois J. Math. 63 (3) 469 - 484, October 2019. https://doi.org/10.1215/00192082-7854872