10 citations · 19 across the 11 of their papers we have counts for
14 papers
Bilinear Kloosterman sums over small boxes and uniformity of a random walk
Ali Mohammadi
Given an additive character of an arbitrary finite field and elements , , we prove a bound on bilinear Kloosterman sums $\s…
On the constant roll complex scalar field inflationary models
Ali Mohammadi, Nahid Ahmadi, Mehdi Shokri
In this paper we wish to point out the possibility of using a complex scalar field in a constant roll inflationary model, as needed for observational viability. We extend the idea…
Product of sets on varieties in finite fields
Che-Jui Chang, Ali Mohammadi, Thang Pham +1
Let be a variety in and . It is known that if any line passing through the origin contains a bounded number of points from , then $|\prod(E)|=|\…
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…
Anti- Transformations And Complex Non-Hermitian -Symmetric Superpartners
Taha Koohrokhi, Sehban Kartal, Ali Mohammadi
We propose a new algebraic formalism for constructing complex non-Hermitian -symmetric superpartners by extending a conventional shape-invariant superpotential into t…
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…
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|, |…
Points on polynomial curves in small boxes modulo an integer
Bryce Kerr, Ali Mohammadi
Given an integer and a polynomial of degree with coefficients in the residue ring we obtain new results concerni…
Improved bounds on Gauss sums in arbitrary finite fields
Ali Mohammadi
Let be a power of a prime and let be the finite field consisting of elements. We establish new explicit estimates on Gauss sums of the form $S_n(a) = \sum_{x…