55 citations · 99 across the 6 of their papers we have counts for
8 papers · 1 filter
Attaining the exponent for the sum-product problem in finite fields
Ali Mohammadi, Sophie Stevens
We improve the exponent in the finite field sum-product problem from to , improving the results of Rudnev, Shakan and Shkredov. That is, we show that if $A\subset \math…
On sum sets of convex functions
Sophie Stevens, Audie Warren
In this paper we prove new bounds for sums of convex or concave functions. Specifically, we prove that for all finite sets, and for all convex or co…
Low-energy decomposition results over finite fields
Ali Mohammadi, Sophie Stevens
We prove various low-energy decomposition results, showing that we can decompose a finite set satisfying , into so that, for a…
The Elekes-Szabó Problem and the Uniformity Conjecture
Mehdi Makhul, Oliver Roche-Newton, Sophie Stevens +1
In this paper we give a conditional improvement to the Elekes-Szabó problem over the rationals, assuming the Uniformity Conjecture. Our main result states that for $F\in \mathbb{Q}…
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…
An Improved Point-Line Incidence Bound Over Arbitrary Fields
Sophie Stevens, Frank de Zeeuw
We prove a new upper bound for the number of incidences between points and lines in a plane over an arbitrary field , a problem first considered by Bourgain, Katz and T…
On The Energy Variant of the Sum-Product Conjecture
Misha Rudnev, Ilya D. Shkredov, Sophie Stevens
We prove new exponents for the energy version of the Erdős-Szemerédi sum-product conjecture, raised by Balog and Wooley. They match the previously established milestone values for…