14 citations · 52 across the 18 of their papers we have counts for
6 papers · 1 filter
Orthogonal systems in vector spaces over finite fields
Alex Iosevich, Steve Senger
We prove that if a subset of the d-dimensional vector space over a finite field is large enough, then it contains many k-tuples of mutually orthogonal vectors.
Extension Theorems for Paraboloids in the Finite Field Setting
Alex Iosevich, Doowon Koh
In this paper we study the boundedness of the extension operators associated with paraboloids in vector spaces over finite fields.In higher even dimensions, we estimate t…
An analog of the Furstenberg-Katznelson-Weiss theorem on triangles in sets of positive density in finite field geometries
David Covert, Derrick Hart, Alex Iosevich +1
We prove that if the cardinality of a subset of the 2-dimensional vector space over a finite field with elements is , with , then it cont…
Extension theorems for the Fourier transform associated with non-degenerate quadratic surfaces in vector spaces over finite fields
Alex Iosevich, Doowon Koh
We study the restriction of the Fourier transform to quadratic surfaces in vector spaces over finite fields. In two dimensions, we obtain the sharp result by considering the sums o…
Distance graphs in vector spaces over finite fields, coloring and pseudo-randomness
Derrick Hart, Alex Iosevich, Doowon Koh +2
In this paper we systematically study various properties of the distance graph in , the -dimensional vector space over the finite field with eleme…
Generalized incidence theorems, homogeneous forms, and sum-product estimates in finite fields
David Covert, Derrick Hart, Alex Iosevich +2
In recent years, sum-product estimates in Euclidean space and finite fields have been studied using a variety of combinatorial, number theoretic and analytic methods. Erdos type pr…