Doowon Koh

activity

20062023

most citedExtension theorems for the Fourier transform associated with non-degenerate quadratic surfaces in vector spaces over finite fields

14 citations · 68 across the 47 of their papers we have counts for

collaborators

Showing math.COShow all

17 papers · 1 filter

math.CO2021

Configurations of rectangles in a set in $F_{q}^{2}$

Doowon Koh, Sujin Lee, Thang Pham +1

Let $F_{q}$ be a finite field of order $q$ . In this paper, we study the distribution of rectangles in a given set in $F_{q}^{2}$ . More precisely, for any $0 < δ \leq 1$ , we…

math.CO2020

A point-sphere incidence bound in odd dimensions and applications

Doowon Koh, Thang Pham

In this paper, we prove a new point-sphere incidence bound in vector spaces over finite fields. More precisely, let $P$ be a set of points and $S$ be a set of spheres in $\mathbb{F…

math.CO2019

On a theorem of Hegyvári and Hennecart

Dao Nguyen Van Anh, Le Quang Ham, Doowon Koh +2

In this paper, we study growth rate of product of sets in the Heisenberg group over finite fields and the complex numbers. More precisely, we will give improvements and extensions…

math.CO2019★ 4 cited

A new perspective on the distance problem over prime fields

Alex Iosevich, Doowon Koh, Thang Pham

Let $F_{p}$ be a prime field, and $E$ a set in $F_{p}^{2}$ . Let $Δ (E) = {∣∣ x - y ∣∣ : x, y \in E}$ , the distance set of $E$ . In…

math.CO2019

Distribution of determinant of sum of matrices

Daewoong Cheong, Doowon Koh, Thang Pham +1

Let $F_{q}$ be an arbitrary finite field of order $q$ . In this article, we study $det S$ for certain types of subsets $S$ in the ring $M_{2} (F_{q})$ of $2 \times 2$ matr…

math.CO2018

A new bound on Erdős distinct distances problem in the plane over prime fields

Alex Iosevich, Doowon Koh, Thang Pham +2

In this paper we obtain a new lower bound on the Erdős distinct distances problem in the plane over prime fields. More precisely, we show that for any set $A \subset F_{p}^{2}$ …

math.CO2018★ 5 cited

On the determinants and permanents of matrices with restricted entries over prime fields

Doowon Koh, Thang Pham, Chun-Yen Shen +1

Let $A$ be a set in a prime field $F_{p}$ . In this paper, we prove that $d \times d$ matrices with entries in $A$ determine almost $∣ A ∣^{3 + \frac{1}{45}}$ distinct determinant…

math.CO2017

Four-variable expanders over the prime fields

Doowon Koh, Hossein Nassajian Mojarrad, Thang Pham +1

Let $F_{p}$ be a prime field of order $p > 2$ , and $A$ be a set in $F_{p}$ with very small size in terms of $p$ . In this note, we show that the number of distinct cubic…

math.CO2017

The generalized k-resultant modulus set problem in finite fields

David Covert, Doowon Koh, Youngjin Pi

Let $F_{q}^{d}$ be the $d$ -dimensional vector space over the finite field $F_{q}$ with $q$ elements. Given $k$ sets $E_{j} \subset F_{q}^{d}$ for $j = 1, 2, \dots, k$ , the…

math.CO2015★ 1 cited

The $k$ -resultant modulus set problem on algebraic varieties over finite fields

David Covert, Doowon Koh, Youngjin Pi

We study the $k$ -resultant modulus set problem in the $d$ -dimensional vector space $F_{q}^{d}$ over the finite field $F_{q}$ with $q$ elements. Given $E\subset \mathbb F_…

math.CO2014★ 1 cited

On the sums of any k points in finite fields

David Covert, Doowon Koh, Youngjin Pi

For a set $E \subset F_{q}^{d}$ , we define the $k$ -resultant magnitude set as $ Δ_k(E) =\{\|\textbf{x}_1 + \dots + \textbf{x}_k\|\in \mathbb F_q: \textbf{x}_1, \dots, \textbf{x}…

math.CO2014

Size of dot product sets determined by pairs of subsets of vector spaces over finite fields

Doowon Koh, Youngjin Pi

In this paper we study the cardinality of the dot product set generated by two subsets of vector spaces over finite fields. We notice that the results on the dot product problems f…

math.CO2012★ 3 cited

Distance sets of two subsets of vector spaces over finite fields

Doowon Koh, Hae-Sang Sun

We investigate the size of the distance set determined by two subsets of finite dimensional vector spaces over finite fields. A lower bound of the size is given explicitly in terms…

math.CO2010

Additive energy and the Falconer distance problem in finite fields

Doowon Koh, Chun-Yen Shen

We study the number of the vectors determined by two sets in d-dimensional vector spaces over finite fields. We observe that the lower bound of cardinality for the set of vectors c…

math.CO2009★ 5 cited

Pinned distance sets, k-simplices, Wolff's exponent in finite fields and sum-product estimates

Jeremy Chapman, M. Burak Erdogan, Derrick Hart +2

An analog of the Falconer distance problem in vector spaces over finite fields asks for the threshold $α > 0$ such that $∣Δ (E) ∣ ≳ q$ whenever $∣ E ∣ ≳ q^{α}$ , where $E \subse…

math.CO2008★ 6 cited

Distance graphs in vector spaces over finite fields, coloring and pseudo-randomness

Derrick Hart, Alex Iosevich, Doowon Koh +2

In this paper we systematically study various properties of the distance graph in $F_{q}^{d}$ , the $d$ -dimensional vector space over the finite field $F_{q}$ with $q$ eleme…

math.CO2008

Generalized incidence theorems, homogeneous forms, and sum-product estimates in finite fields

David Covert, Derrick Hart, Alex Iosevich +2

In recent years, sum-product estimates in Euclidean space and finite fields have been studied using a variety of combinatorial, number theoretic and analytic methods. Erdos type pr…

Configurations of rectangles in a set in Fq2​

A point-sphere incidence bound in odd dimensions and applications

On a theorem of Hegyvári and Hennecart

A new perspective on the distance problem over prime fields

Distribution of determinant of sum of matrices

A new bound on Erdős distinct distances problem in the plane over prime fields

On the determinants and permanents of matrices with restricted entries over prime fields

Four-variable expanders over the prime fields

The generalized k-resultant modulus set problem in finite fields

The k-resultant modulus set problem on algebraic varieties over finite fields

On the sums of any k points in finite fields

Size of dot product sets determined by pairs of subsets of vector spaces over finite fields

Distance sets of two subsets of vector spaces over finite fields

Additive energy and the Falconer distance problem in finite fields

Pinned distance sets, k-simplices, Wolff's exponent in finite fields and sum-product estimates

Distance graphs in vector spaces over finite fields, coloring and pseudo-randomness

Generalized incidence theorems, homogeneous forms, and sum-product estimates in finite fields

Configurations of rectangles in a set in $F_{q}^{2}$

The $k$ -resultant modulus set problem on algebraic varieties over finite fields