52 citations · 127 across the 37 of their papers we have counts for
4 papers · 1 filter
Convexity and a sum-product type estimate
Liangpan Li, Oliver Roche-Newton
In this paper we further study the relationship between convexity and additive growth, building on the work of Schoen and Shkredov (\cite{SS}) to get some improvements to earlier r…
An improved sum-product estimate over finite fields
Liangpan Li, Oliver Roche-Newton
This paper gives an improved sum-product estimate for subsets of a finite field whose order is not prime. It is shown, under certain conditions, that $$\max\{|A+A|,|A\cdot{A}|\}\gg…
On an application of Guth-Katz theorem
Alex Iosevich, Oliver Roche-Newton, Misha Rudnev
We prove that for some universal , a non-collinear set of points in the Euclidean plane determines at least distinct areas of triangles with…
An improved sum-product estimate for general finite fields
Oliver Roche-Newton
This paper improves on a sum-product estimate obtained by Katz and Shen for subsets of a finite field whose order is not prime.