52 citations · 222 across the 27 of their papers we have counts for
32 papers · 1 filter
Multiplicative Subgroups of Prime Fields Are Not Sumsets
Misha Rudnev, Fred Tyrrell
Let be a proper multiplicative subgroup, and suppose that for some . We prove that either one of the summands is a sin…
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…
An Energy Bound in the Affine Group
Giorgis Petridis, Oliver Roche-Newton, Misha Rudnev +1
We prove a nontrivial energy bound for a finite set of affine transformations over a general field and discuss a number of implications. These include new bounds on growth in the a…
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…
On the number of hinges defined by a point set in
Misha Rudnev
It is shown that the number of distinct types of three-point hinges, defined by a real plane set of points is , where a hinge is identified by fixing two pa…
On growth rate in , the affine group and sum-product type implications
Misha Rudnev, Ilya D. Shkredov
This paper aims to study in more depth the relation between growth in matrix groups and over a field by multiplication…