52 citations · 123 across the 14 of their papers we have counts for
20 papers
On Korobov bound concerning Zaremba's conjecture
Nikolay Moshchevitin, Brendan Murphy, Ilya Shkredov
We prove in particular that for any sufficiently large prime there is such that all partial quotients of are bounded by . For composite…
Growth in linear groups
Sean Eberhard, Brendan Murphy, László Pyber +1
We prove a conjecture of Helfgott on the structure of sets of bounded tripling in bounded rank, which states the following. Let be a finite symmetric subset of $\mathrm{GL}_n(\…
Growth in Some Finite Three-Dimensional Matrix Groups
Brendan Murphy, James Wheeler
We study the growth of product sets in some finite three-dimensional matrix groups. In particular, we prove two results about the group of upper triangular matrices ove…
On the Pinned Distances Problem in Positive Characteristic
Brendan Murphy, Giorgis Petridis, Thang Pham +2
We study the Erd\H os-Falconer distance problem for a set , where is a field of positive characteristic . If and th…
Bisector energy and pinned distances in positive characteristic
Brendan Murphy, Misha Rudnev, Sophie Stevens
We prove a new lower bound for the number of pinned distances over finite fields: if is a sufficiently small subset of , then there is an element in that de…
Group Action Combinatorics
Brendan Murphy
This paper generalizes the basic notions of additive and multiplicative combinatorics to the setting of group actions: if is a group acting on a set , and we have subsets $A…