14 citations · 52 across the 18 of their papers we have counts for
6 papers · 1 filter
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…
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…
Sums and products in finite fields: an integral geometric viewpoint
Derrick Hart, Alex Iosevich
We prove that if is such that then where $$A^2=\{a \cdot a': a,a'…
Ubiquity of simplices in subsets of vector spaces over finite fields
Derrick Hart, Alex Iosevich
We prove that a sufficiently large subset of the -dimensional vector space over a finite field with elements, , contains a copy of every -simplex. Fourier…