Bo Tan

activity

20242026

collaborators

9 papers

math.NT2026

Metric Poissonian Pair Correlation Property Part 1: The Case $n+\log n$

Bo Tan, Zhen Zhang, Qing-Long Zhou

We prove that $(α (n + lo g n))_{n \geq 1}$ has Poissonian pair correlation for Lebesgue almost every real $α$ . This solves a Problem posed by Aistleitner, El-Baz and Munsch [Open Proble…

math.NT2026

Metric Poissonian Pair Correlation Property Part 2: The Case $n\log n$

Bo Tan, Zhen Zhang, Qing-Long Zhou

We prove that $(α n lo g n)_{n \geq 1}$ has Poissonian pair correlation for almost every real $α$ , solving a Problem posed by Aistleitner, El-Baz and Munsch [Open Problem 3, Geom. Funct…

math.NT2026

Poissonian Pair Correlation for Bernoulli Orbits

Bo Tan, Zhen Zhang, Qing-Long Zhou

Let $α, β\in \mathbb{T} = \mathbb{R}/\mathbb{Z}$, and let $(ξ_n)_{n \ge 1}$ be independent random variables taking the values $α$ and $β$ with equal probability. We study t…

math.NT2026

Fourier Dimension in Inhomogeneous Duffin--Schaeffer Conjecture

Bo Tan, Qing-Long Zhou

Let $Q \subseteq \mathbb{N}$ be a subset, and let $ψ\colon \mathbb{N} \to [0, \tfrac{1}{2})$, $θ\colon \mathbb{N} \to \mathbb{R}$ be functions. Let $\{A_q\}$ and \(\{B_q\}\…

math.NT2025

Hausdorff measures of sets in Exact Diophantine approximation

Bo Tan, Chen Tian, Baowei Wang +1

Let $(X, d)$ be a compact metric space, and let $Q \subset X$ be countable. Given functions $R : Q \to R^{+}$ and $ϕ : R^{+} \to R^{+}$ , we consider the set $E(Q…

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\…

Metric Poissonian Pair Correlation Property Part 1: The Case \(n+\log n\)

Metric Poissonian Pair Correlation Property Part 2: The Case \(n\log n\)

Poissonian Pair Correlation for Bernoulli Orbits

Fourier Dimension in Inhomogeneous Duffin--Schaeffer Conjecture

Hausdorff measures of sets in Exact Diophantine approximation

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

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

Non-Salem sets in multiplicative Diophantine approximation

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

Metric Poissonian Pair Correlation Property Part 1: The Case \(n+\log n\)

Metric Poissonian Pair Correlation Property Part 2: The Case \(n\log n\)

Poissonian Pair Correlation for Bernoulli Orbits

Fourier Dimension in Inhomogeneous Duffin--Schaeffer Conjecture

Hausdorff measures of sets in Exact Diophantine approximation

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 $R^{2}$