Qinglong Zhou

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math.NT2025

Twisted Diophantine approximation for matrix transformations of tori

Sam Chow, Qing-Long Zhou

Consider a sequence of integral matrices $A = (A_{n})_{n \in N}$ , and a $d$ -tuple function $r = (r_{1}, \dots, r_{d}) : N \to (0, \frac{1}{2})$ . For a fixed vector ${\bm α},…

math.NT2025

Quantitative Matrix-Driven Diophantine approximation on $M_{0}$ -sets

Bo Tan, Qing-Long Zhou

Let $E \subset [0, 1)^{d}$ be a set supporting a probability measure $μ$ with Fourier decay $∣ μ (t) ∣ ≪ (lo g ∣ t ∣)^{- s}$ for some constant $s > d + 1.$ Consider a se…

math.NT2024

Exact Diophantine approximation $:$ the simultaneous case in $R^{2}$

Bo Tan, Qing-Long Zhou

We fill a gap in the study of the Hausdorff dimension of the set of exact approximation order considered by Fregoli [Proc. Amer. Math. Soc. 152 (2024), no. 8, 3177--3182].

math.NT2024

Non-Salem sets in multiplicative Diophantine approximation

Bo Tan, Qing-Long Zhou

In this paper, we answer a question of Cai-Hambrook in (arXiv $:$ 2403.19410). Furthermore, we compute the Fourier dimension of the multiplicative $ψ$ -well approximable set $$M…

math.NT2024

Quantitative Diophantine approximation and Fourier dimension of sets: Dirichlet non-improvable numbers versus well-approximable numbers

Bo Tan, Qing-Long Zhou

Let $E \subset [0, 1]$ be a set that supports a probability measure $μ$ with the property that $∣ μ (t) ∣ ≪ (lo g ∣ t ∣)^{- A}$ for some constant $A > 2.$ Let $\mathcal{A}=(q_n)_{n\…

Twisted Diophantine approximation for matrix transformations of tori

Quantitative Matrix-Driven Diophantine approximation on M0​-sets

Exact Diophantine approximation: the simultaneous case in R2

Non-Salem sets in multiplicative Diophantine approximation

Quantitative Diophantine approximation and Fourier dimension of sets: Dirichlet non-improvable numbers versus well-approximable numbers

Quantitative Matrix-Driven Diophantine approximation on $M_{0}$ -sets

Exact Diophantine approximation $:$ the simultaneous case in $R^{2}$