10 citations · 19 across the 11 of their papers we have counts for
7 papers · 1 filter
A Point-Conic Incidence Bound and Applications over
Ali Mohammadi, Thang Pham, Audie Warren
In this paper, we prove the first incidence bound for points and conics over prime fields. As applications, we prove new results on expansion of bivariate polynomial images and on…
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…
Almost orthogonal subsets of vector spaces over finite fields
Ali Mohammadi, Giorgis Petridis
We prove various results on the size and structure of subsets of vector spaces over finite fields which, in some sense, have too many mutually orthogonal pairs of vectors. In parti…
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…
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|, |…