6 papers
Sharp refined-direction Kakeya estimates in finite Heisenberg groups
Thang Pham, Andrea Pinamonti, Dung The Tran +1
Let and let be an odd prime power. The first aim of this paper is to prove that, for every and every , the following sharp…
ErdÅs--Falconer distance conjecture from an analytic perspective
Le Quang Ham, Dung The Tran
Let \(q\) be an odd prime power and let \(V=\F_q^{2m}\), equipped with \(Q(x)=x_1^2+\cdots+x_{2m}^2\). We develop a semidefinite Delsarte framework for the two-set ErdÅs--Falconer…
Horizontal Kakeya maximal operators in finite Heisenberg groups: Exact exponents and applications
Thang Pham, Andrea Pinamonti, Dung The Tran +1
Let be an odd prime power. We study Kakeya maximal operators associated with horizontal lines in the finite Heisenberg groups . Our principal object i…
Raimi's theorem for manifolds with circle symmetry
Dung The Tran
Raimi's classical theorem establishes a partition of the natural numbers with a remarkable unavoidability property: for every finite coloring of , there is a color clas…
Parabolic distance in : a sharp exponent and new results
Dao Nguyen Van Anh, Steven Senger, Dung The Tran +1
We study the parabolic variant of the Erd\H os--Falconer distance problem in finite fields. That is, if is odd, we seek size thresholds beyond which any subset $E\subset \mathb…
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 grou…