Sphere intersections and incidences over finite fields
Combinatorics
2025-10-01 v1
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.
Cite
@article{arxiv.2509.25997,
title = {Sphere intersections and incidences over finite fields},
author = {Doowon Koh and Ben Lund and Chuandong Xu and Semin Yoo},
journal= {arXiv preprint arXiv:2509.25997},
year = {2025}
}