F. Rakhmonov

collaborators

6 papers

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 ErdÅs-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 $I^ (A, B)$ 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.CO2024

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 $I^ (E) := {∥ x - y ∥ : x, y \in E}$ , where $\lVer…

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…

Lp averages of the discrete Fourier transform and applications

The ErdÅs-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

Distribution of similar configurations in subsets of Fqd​

Similar point configurations via group actions

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

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

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

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