5 papers
Raimi's theorem for the -dimensional torus
Hunseok Kang, Doowon Koh, Dung The Tran
We extend Raimi's classical partition theorem to the continuous setting of the circle and -dimensional torus. Building on recent work of Hegyvári, Pach, and Pham in finite group…
Restricted projections in positive characteristic via Fourier extension and restriction estimates
Le Quang Ham, Do Trong Hoang, Le Quang Hung +2
Let and be the -dimensional vector space over a finite field of order , where is an odd prime power. Let be the set of lines through th…
Sphere intersections and incidences over finite fields
Doowon Koh, Ben Lund, Chuandong Xu +1
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 ob…
The Erdős-Falconer distance problem between arbitrary sets and -coordinatable sets in finite fields
Hunseok Kang, Doowon Koh, Firdavs Rakhmonov
In this paper, we study the cardinality of the distance set determined by two subsets and of the -dimensional vector space over a finite field .…
Connections between -operators and restriction estimates for spheres over finite fields
Hunseok Kang, Doowon Koh
In this paper, we introduce a new operator, , which is closely related to the restriction problem for spheres in , the -dimensional vector space ove…