Ayreena Bakhtawar

activity

20182026

most citedHausdorff dimension of a set in the theory of continued fractions

21 citations · 37 across the 12 of their papers we have counts for

collaborators

13 papers

math.DS2026

Sharpening Borel's result in Diophantine approximation

Savita S. Adhin, Ayreena Bakhtawar, Cor Kraaikamp

In this paper, we refine Borel's 1903 result in Diophantine approximation by providing sharper bounds for the minimum of three consecutive approximation coefficients $Θ_{n} (x)$ , defi…

math.DS2026

On the minimum of $σ$ -Brjuno functions

Ayreena Bakhtawar, Carlo Carminati, Stefano Marmi

$σ$ -Brjuno functions were introduced in \cite{MaMoYo_06} as an interesting variant of the classical Brjuno function, where one substitutes the $lo g$ singularity at $x = 0$ with the…

math.DS2025

Hausdorff dimension for the weighted products of multiple digits in d-decaying Gauss like systems

Ayreena Bakhtawar, Michał Rams

We compute the Hausdorff dimension of sets defined by the growth of weighted products of multiple digits at arbitrary positions in $d$ -decaying Gauss-like iterated function systems…

math.DS2025

Sharpening Vahlen's result in Diophantine approximation

Ayreena Bakhtawar, Cor Kraaikamp

n this paper we refine Vahlen's 1895 result in Diophantine approximation by providing sharper bounds for the approximation coefficients, especially when at least one of the partial…

math.NT2025

Uniform Diophantine approximation on the Hecke group $H_{4}$

Ayreena Bakhtawar, Dong Han Kim, Seul Bee Lee

Dirichlet's uniform approximation theorem is a fundamental result in Diophantine approximation that gives an optimal rate of approximation with a given bound. We study uniform Diop…

math.DS2024

Regularity properties of the $α$ -Wilton functions

Ayreena Bakhtawar, Carlo Carminati, Seul Bee Lee

The aim of this article is to study the regularity properties of the Wilton functions $W_{α}$ associated with $α$ -continued fractions. We prove that the Wilton function is BMO for $α…

math.DS2024

Global and local minima of $α$ -Brjuno functions

Ayreena Bakhtawar, Carlo Carminati, Stefano Marmi

The main goal of this article is to analyze some peculiar features of the global (and local) minima of $α$ -Brjuno functions $B_{α}$ where $α \in (0, 1] .$ Our starting point is the resul…

math.NT2022★ 7 cited

Increasing rate of weighted product of partial quotients in continued fractions

Ayreena Bakhtawar, Jing Feng

Let $[a_{1} (x), a_{2} (x), \dots, a_{n} (x), \dots]$ be the continued fraction expansion of $x \in [0, 1)$ . In this paper, we study the increasing rate of the weighted product $a^{t_0}_n(x)a^{t…

math.NT2022★ 5 cited

Metrical properties for the weighted products of multiple partial quotients in continued fractions

Ayreena Bakhtawar, Mumtaz Hussain, Dmitry Kleinbock +1

The classical Khintchine and Jarník theorems, generalizations of a consequence of Dirichlet's theorem, are fundamental results in the theory of Diophantine approximation. These the…

math.NT2022

Generalised Hausdorff measure of sets of Dirichlet non-improvable matrices in higher dimensions

Ayreena Bakhtawar, David Simmons

Let $ψ : R_{+} \to R_{+}$ be a nonincreasing function. A pair $(A, b),$ where $A$ is a real $m \times n$ matrix and $b \in R^{m},$ is said to be $ψ…

math.NT2019

Hausdorff dimension for the set of points connected with the generalized Jarník-Besicovitch set

Ayreena Bakhtawar

In this article we aim to investigate the Hausdorff dimension of the set of points $x \in [0, 1)$ such that for any $r \in N,$ \begin{align*} a_{n+1}(x)a_{n+2}(x)\cdots a_{n+…

math.DS2019★ 21 cited

Hausdorff dimension of a set in the theory of continued fractions

Ayreena Bakhtawar, Philip Bos, Mumtaz Hussain

In this article we calculate the Hausdorff dimension of the set \begin{equation*} \mathcal{F}(Φ)=\left\{ x\in \lbrack 0,1):\begin{aligned}a_{n+1}(x)a_n(x) \geq Φ(n) \ {\rm for \ in…

math.NT2018★ 4 cited

The sets of Dirichlet non-improvable numbers vs well-approximable numbers