7 papers
An energy decomposition theorem for matrices and related questions
Ali Mohammadi, Thang Pham, Yiting Wang
Given , we prove that there exist disjoint subsets such that and their additive and multiplicative energies satisf…
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…
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…
Szemerédi-Trotter type results in arbitrary finite fields
Ali Mohammadi
Let be a power of a prime and the finite field consisting of elements. We prove explicit upper bounds on the number of incidences between lines and Cartesian…
On growth of the set in arbitrary finite fields
Ali Mohammadi
Let be a finite field of order , where is a power of a prime. For a set , under certain structural restrictions, we prove a new explic…
A new sum-product estimate in prime fields
Changhao Chen, Bryce Kerr, Ali Mohammadi
In this paper we obtain a new sum-product estimate in prime fields. In particular, we show that if satisfies then $$ \max\{|A\pm A|, |…