Alex Iosevich

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math.CA2005

Erdos distance problem in vector spaces over finite fields

Alex Iosevich, Misha Rudnev

We study the Erdös/Falconer distance problem in vector spaces over finite fields. Let $F_{q}$ be a finite field with $q$ elements and take $E \subset F_{q}^{d}$ , $d \geq 2$ .…

math.CA2004

Endpoint bounds for the non-isotropic Falconer distance problem associated with lattice-like sets

A. Iosevich, M. Rudnev

Let $S \subset R^{d}$ be contained in the unit ball. Let $Δ (S) = {∣∣ a - b ∣∣ : a, b \in S}$ , the Euclidean distance set of $S$ . Falconer conjectured that the $Δ (S)$ has positive…