Sphere intersections and incidences over finite fields
Doowon Koh, Ben Lund, Chuandong Xu, Semin Yoo
Published: 2025/9/30
Abstract
We bound the number of incidences between points and spheres in finite vector spaces by bounding the sum of the number of points in the pairwise intersections of the spheres. We obtain new incidence bounds that are interesting when the number of spheres is not too large. Our approach also leads to an elementary proof of the Iosevich-Rudnev bound on the Erd\H{o}s-Falconer distance problem in odd dimensions.