46 citations · 413 across the 115 of their papers we have counts for
8 papers · 1 filter
Extension Theorems for Spheres in the Finite Field Setting
Alex Iosevich, Doowon Koh
In this paper we study the boundedness of extension operators associated with spheres in vector spaces over finite fields.In even dimensions, we estimate the number of incidences b…
Pinned distance sets, Wolff's exponent in finite fields and improved sum-product estimates
Derrick Hart, Alex Iosevich
An analog of the Falconer distance problem in vector spaces over finite fields asks for the threshold such that whenever , where $E \subse…
A universal Stein-Tomas restriction estimate for measures in three dimensions
Alex Iosevich, Svetlana Roudenko
We study restriction estimates in R^3 for surfaces given as graphs of W^1_1(R^2) (integrable gradient) functions. We obtain a "universal" L^2(mu) -> L^4(R^3, L^2(SO(3))) estimate f…
Distances sets that are a shift of the integers and Fourier basis for planar convex sets
Alex Iosevich, Philippe Jaming
The aim of this paper is to prove that if a planar set has a difference set satisfying for suitable than has at most 3 elements. This result…
Averages over hyperplanes, sum-product theory in vector spaces over finite fields and the Erdos-Falconer distance conjecture
Derrick Hart, Alex Iosevich, Doowon Koh +1
We prove a point-wise and average bound for the number of incidences between points and hyper-planes in vector spaces over finite fields. While our estimates are, in general, sharp…
Theory of dimension for large discrete sets and applications
Alex Iosevich, Misha Rudnev, Ignacio Uriarte-Tuero
We define two notions of discrete dimension based on the Minkowski and Hausdorff dimensions in the continuous setting. After proving some basic results illustrating these definitio…