F. Rakhmonov

activity

20222026

most citedDistribution of similar configurations in subsets of

F_{q}^{d}

2 citations · 2 across the 9 of their papers we have counts for

collaborators

9 papers

math.CO2026

Majorization and additive tuples in $Z_{2}^{n}$

Sophie Huczynska, Firdavs Rakhmonov, Chi Hoi Yip

Majorization is a fundamental tool for comparing how "spread out" the entries of two vectors are. Key majorization results were obtained for the integers by Hardy, Littlewood and P…

math.CO2025

$L^{p}$ averages of the discrete Fourier transform and applications

Jonathan M. Fraser, Firdavs Rakhmonov

The discrete Fourier transform has proven to be an essential tool in many geometric and combinatorial problems in vector spaces over finite fields. In general, sets with good unifo…

math.CO2025

The Erdős-Falconer distance problem between arbitrary sets and $k$ -coordinatable sets in finite fields

Hunseok Kang, Doowon Koh, Firdavs Rakhmonov

In this paper, we study the cardinality of the distance set $Δ (A, B)$ determined by two subsets $A$ and $B$ of the $d$ -dimensional vector space over a finite field $F_{q}$ .…

math.CO2025

An improved $L^{2}$ restriction theorem in finite fields

Jonathan M. Fraser, Firdavs Rakhmonov

Mockenhaupt and Tao (Duke 2004) proved a finite field analogue of the Stein--Tomas restriction theorem, establishing a range of $q$ for which $L^{q} \to L^{2}$ restriction estimates hol…

math.CO2025

Exceptional projections in finite fields: Fourier analytic bounds and incidence geometry

Jonathan M. Fraser, Firdavs Rakhmonov

We consider the problem of bounding the number of exceptional projections (projections which are smaller than typical) of a subset of a vector space over a finite field onto subspa…

math.CA2024

Similar point configurations via group actions

P. Bhowmik, A. Greenleaf, A. Iosevich +2

We prove that for $d \geq 2, k \geq 2$ , if the Hausdorff dimension of a compact set $E \subset R^{d}$ is greater than $\frac{d ^{2}}{2 d - 1}$ , then, for any given $r > 0$ , there exi…

math.CO2023

Near optimal thresholds for existence of dilated configurations in $F_{q}^{d}$

Pablo Bhowmik, Firdavs Rakhmonov

Let $E \subset F_{q}^{d}$ and $∥ \cdot ∥ : F_{q}^{d} \to F_{q}$ defined as $∥ α ∥ := α_{1}^{2} + \dots + α_{d}^{2}$ if $α = (α_{1}, \dots, α_{d}) \in F_{q}^{d}$ , wher…

math.NT2023

The quotient set of the quadratic distance set over finite fields

Alex Iosevich, Doowon Koh, Firdavs Rakhmonov

Let $F_{q}^{d}$ be the $d$ -dimensional vector space over the finite field $F_{q}$ with $q$ elements. For each non-zero $r$ in $F_{q}$ and $E \subset F_{q}^{d}$ ,…

math.CO2022★ 2 cited

Distribution of similar configurations in subsets of $F_{q}^{d}$

Firdavs Rakhmonov

Let $F_{q}$ be a finite field of order $q$ and $E$ be a set in $F_{q}^{d}$ . The distance set of $E$ is defined by $Δ (E) := {∥ x - y ∥ : x, y \in E}$ , where $\lVert…

Majorization and additive tuples in Z2n​

Lp averages of the discrete Fourier transform and applications

The Erdős-Falconer distance problem between arbitrary sets and k-coordinatable sets in finite fields

An improved L2 restriction theorem in finite fields

Exceptional projections in finite fields: Fourier analytic bounds and incidence geometry

Similar point configurations via group actions

Near optimal thresholds for existence of dilated configurations in Fqd​

The quotient set of the quadratic distance set over finite fields

Distribution of similar configurations in subsets of Fqd​

Majorization and additive tuples in $Z_{2}^{n}$

$L^{p}$ averages of the discrete Fourier transform and applications

The Erdős-Falconer distance problem between arbitrary sets and $k$ -coordinatable sets in finite fields

An improved $L^{2}$ restriction theorem in finite fields

Near optimal thresholds for existence of dilated configurations in $F_{q}^{d}$

Distribution of similar configurations in subsets of $F_{q}^{d}$