52 citations · 127 across the 37 of their papers we have counts for
7 papers · 1 filter
Constructions for the Elekes-Szabó and Elekes-Rónyai problems
Mehdi Makhul, Oliver Roche-Newton, Audie Warren +1
We give a construction of a non-degenerate polynomial and a set of cardinality such that $\left|Z(F)\cap (A \times A \times A) \right| \gg n^{\frac{…
An improved bound for the size of the set
Oliver Roche-Newton
It is established that for any finite set of positive real numbers , we have
If is small then is superquadratic
Oliver Roche-Newton, Ilya D. Shkredov
This note proves that there exists positive constants and such that for all finite with we have .
On iterated product sets with shifts II
Brandon Hanson, Oliver Roche-Newton, Dmitrii Zhelezov
The main result of this paper is the following: for all there exists such that \[ \max \{ |A^{(k)}|, |(A+u)^{(k)}| \} \geq |A|^b, \] for any finite $A \s…
Improved Bounds for Pencils of Lines
Oliver Roche-Newton, Audie Warren
We consider a question raised by Rudnev: given four pencils of concurrent lines in , with the four centres of the pencils non-collinear, what is the maximum possib…
On the size of the set
Oliver Roche-Newton, Imre Z. Ruzsa, Chun-Yen Shen +1
It is established that there exists an absolute constant such that for any finite set of positive real numbers On the other hand, we g…
On iterated product sets with shifts
Brandon Hanson, Oliver Roche-Newton, Dmitrii Zhelezov
We prove that, for any finite set with and any positive integer , the -fold product set of the shift satisfies the bound $$| \{(a…