11 citations · 20 across the 5 of their papers we have counts for
5 papers
A short proof of a near-optimal cardinality estimate for the product of a sum set
Oliver Roche-Newton
In this note it is established that, for any finite set of real numbers, there exist two elements such that In particul…
A bound on the multiplicative energy of a sum set and extremal sum-product problems
Oliver Roche-Newton, Dmitry Zhelezov
In recent years some near-optimal estimates have been established for certain sum-product type estimates. This paper gives some first extremal results which provide information abo…
Sum-ratio estimates over arbitrary finite fields
Oliver Roche-Newton
The aim of this note is to record a proof that the estimate holds for any set , provided that satisfies certai…
Improved bounds on the set A(A+1)
Timothy G. F. Jones, Oliver Roche-Newton
For a subset A of a field F, write A(A + 1) for the set {a(b + 1):a,b\in A}. We establish new estimates on the size of A(A+1) in the case where F is either a finite field of prime…
On the Minkowski distances and products of sum sets
Oliver Roche-Newton, Misha Rudnev
Given two points in the real plane, the signed area of the rectangle with the diagonal equals the square of the Minkowski distance between the points . We prove t…