additive combinatorics 1Erdős-Falconer distance 1finite fields 1Kloosterman sums 1spherical restriction 1
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math.CA2026
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…
math.CA2026
On the prime field spherical restriction conjecture in four dimensions: breaking the Stein-Tomas exponent and applications
Thang Pham, Boqing Xue
The paper develops a new slicing and stopping‑time decomposition technique to break the Stein‑Tomas exponent for the spherical restriction problem over prime fields in four dimensi…
math.CA2026
On Fourier decay and the distance set problem
Jonathan M. Fraser, Thang Pham
We study the Falconer distance set problem in Euclidean space and obtain improved dimensional estimates under natural Fourier analytic assumptions cast in terms of the Fourier dime…