Doowon Koh

collaborators

7 papers

math.CA2026

Mapping properties of the $S$ -operator

Hunseok Kang, Doowon Koh, Changhun Yang

In this paper, we study the $ℓ^{p} \to ℓ^{r}$ estimates for the $S$ -operator arising in restriction problems for spheres over finite fields. We establish a necessary and sufficien…

math.CO2025

Raimi's theorem for the $n$ -dimensional torus

Hunseok Kang, Doowon Koh, Dung The Tran

We extend Raimi's classical partition theorem to the continuous setting of the circle and $n$ -dimensional torus. Building on recent work of Hegyvári, Pach, and Pham in finite group…

math.CO2025

Additive structures imply more distances in $F_{q}^{d}$

Daewoong Cheong, Gennian Ge, Doowon Koh +3

For a set $E \subseteq F_{q}^{d}$ , the distance set is defined as $Δ (E) := {∥ x - y ∥ : x, y \in E}$ , where $∥ \cdot ∥$ denotes the stand…

math.CO2025

Restricted projections in positive characteristic via Fourier extension and restriction estimates

Le Quang Ham, Do Trong Hoang, Le Quang Hung +2

Let $d \geq 3$ and $F_{q}^{d}$ be the $d$ -dimensional vector space over a finite field of order $q$ , where $q$ is an odd prime power. Let $X_{π}$ be the set of lines through th…

math.CO2025

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…

math.CO2025

The Erdős-Falconer distance problem between arbitrary sets and $k$ -coordinatable sets in finite fields

Hunseok Kang, Doowon Koh, Firdavs Rakhmonov

In this paper, we study the cardinality of the distance set $Δ (A, B)$ determined by two subsets $A$ and $B$ of the $d$ -dimensional vector space over a finite field $F_{q}$ .…

math.CA2025

Connections between $S$ -operators and restriction estimates for spheres over finite fields

Hunseok Kang, Doowon Koh

In this paper, we introduce a new operator, $S$ , which is closely related to the restriction problem for spheres in $F_{q}^{d}$ , the $d$ -dimensional vector space ove…

Mapping properties of the S-operator

Raimi's theorem for the n-dimensional torus

Additive structures imply more distances in Fqd​

Restricted projections in positive characteristic via Fourier extension and restriction estimates

Sphere intersections and incidences over finite fields

The Erdős-Falconer distance problem between arbitrary sets and k-coordinatable sets in finite fields

Connections between S-operators and restriction estimates for spheres over finite fields

Mapping properties of the $S$ -operator

Raimi's theorem for the $n$ -dimensional torus

Additive structures imply more distances in $F_{q}^{d}$

The Erdős-Falconer distance problem between arbitrary sets and $k$ -coordinatable sets in finite fields

Connections between $S$ -operators and restriction estimates for spheres over finite fields