46 citations · 413 across the 115 of their papers we have counts for
6 papers · 1 filter
Fourier integral operators, fractal sets and the regular value theorem
Suresh Eswarathasan, Alex Iosevich, Krystal Taylor
We prove that if , , is an Ahlfors-David regular product set of sufficiently large Hausdorff dimension, denoted by $dim_{\mathcal H}({\…
On directions determined by subsets of vector spaces over finite fields
Alex Iosevich, Hannah Morgan, Jonathan Pakianathan
We prove that if a subset of a -dimensional vector space over a finite field with elements has more than elements, then it determines all the possible directions.…
A Furstenberg-Katznelson-Weiss type theorem on (d + 1)-point configurations in sets of positive density in finite field geometries
David Covert, Derrick Hart, Alex Iosevich +2
We show that if , the -dimensional vector space over the finite field with elements, and , where , the…
On sets of directions determined by subsets of
Alex Iosevich, Mihalis Mourgoglou, Steven Senger
Given , , define the set of directions determined by . We prove that if the H…
On three point configurations determined by subsets of the Euclidean plane, the associated bilinear operator and applications to discrete geometry
Allan Greenleaf, Alex Iosevich
We prove that if the Hausdorff dimension of a compact set is greater than 7/4, then the set of {\ag three-point configurations determined by has positive…
Sharpness of Falconer's estimate in continuous and arithmetic settings, geometric incidence theorems and distribution of lattice points in convex domains
Alex Iosevich, Steven Senger
In this paper we prove, for all , that for no does imply the canonical Falconer distance problem incidence bound, or the analogous estima…