T. Pham

activity

20142023

most citedOn the Pinned Distances Problem in Positive Characteristic

29 citations · 64 across the 45 of their papers we have counts for

collaborators

Showing 2021Show all

9 papers · 1 filter

math.NT2021

Structural theorems on the distance sets over finite fields

Doowon Koh, Minh Quy Pham, Thang Pham

Let $F_{q}$ be a finite field of order $q$ . Iosevich and Rudnev (2005) proved that for any set $A \subset F_{q}^{d}$ , if $∣ A ∣ ≫ q^{\frac{d + 1}{2}}$ , then the distance se…

math.CO2021★ 1 cited

A Point-Conic Incidence Bound and Applications over $F_{p}$

Ali Mohammadi, Thang Pham, Audie Warren

In this paper, we prove the first incidence bound for points and conics over prime fields. As applications, we prove new results on expansion of bivariate polynomial images and on…

math.CO2021

An energy decomposition theorem for matrices and related questions

Ali Mohammadi, Thang Pham, Yiting Wang

Given $A \subseteq G L_{2} (F_{q})$ , we prove that there exist disjoint subsets $B, C \subseteq A$ such that $A = B ⊔ C$ and their additive and multiplicative energies satisf…

math.CA2021

Falconer type functions in three variables

Doowon Koh, Thang Pham, Chun-Yen Shen

Let $f \in R [x, y, z]$ be a quadratic polynomial that depends on each variable and that does not have the form $g (h (x) + k (y) + l (z))$ . Let $A, B, C$ be compact sets in $\mathb…

math.CO2021

Distribution of distances in five dimensions and related problems

Francois Clement, Thang Pham

In this paper, we study the Erdős-Falconer distance problem in five dimensions for sets of Cartesian product structures. More precisely, we show that for $A \subset F_{p}$ wi…

math.CA2021

Mattila--Sjölin type functions: A finite field model

Daewoong Cheong, Doowon Koh, Thang Pham +1

Let $ϕ (x, y) : R^{d} \times R^{d} \to R$ be a function. We say $ϕ$ is a Mattila--Sjölin type function of index $γ$ if $γ$ is the smallest number satisfying…