7 citations · 14 across the 11 of their papers we have counts for
4 papers · 1 filter
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…
Conical Kakeya and Nikodym Sets in Finite Fields
Audie Warren, Arne Winterhof
A Kakeya set contains a line in each direction. Dvir proved a lower bound on the size of any Kakeya set in a finite field using the polynomial method. We prove analogues of Dvir's…
New Expander Bounds from Affine Group Energy
Oliver Roche-Newton, Audie Warren
The purpose of this article is to further explore how the structure of the affine group can be used to deduce new incidence theorems, and to explore sum-product type applications o…
On Products of Shifts in Arbitrary Fields
Audie Warren
We adapt the approach of Rudnev, Shakan, and Shkredov to prove that in an arbitrary field , for all finite with if $p:= Char(\mat…