Steven Senger

most citedSharpness of Falconer's estimate in continuous and arithmetic settings, geometric incidence theorems and distribution of lattice points in convex domains

9 citations · 10 across the 5 of their papers we have counts for

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math.CO2012

A note on the multiplicative structure of an additively shifted product set, AA+1

Steven Senger

We consider the multiplicative structure of sets of the form AA+1, where where A is a large, finite set of real numbers. In particular, we show that the additively shifted product…

math.CO2010

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 $E \subset F_{q}^{d}$ , the $d$ -dimensional vector space over the finite field with $q$ elements, and $∣ E ∣ \geq ρ q^{d}$ , where $q^{- \frac{1}{2}} ≪ ρ \leq 1$ , the…

math.CO2010★ 9 cited

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 $d \geq 2$ , that for no $s < \frac{d + 1}{2}$ does $I_{s} (μ) < \infty$ imply the canonical Falconer distance problem incidence bound, or the analogous estima…