6 papers
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…
Twisted Diophantine approximation for matrix transformations of tori
Sam Chow, Qing-Long Zhou
Consider a sequence of integral matrices , and a -tuple function . For a fixed vector ${\bm α},…
Quantitative Matrix-Driven Diophantine approximation on -sets
Bo Tan, Qing-Long Zhou
Let be a set supporting a probability measure with Fourier decay for some constant Consider a se…
Exact Diophantine approximation the simultaneous case in
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].
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 -well approximable set $$M…
Quantitative Diophantine approximation and Fourier dimension of sets: Dirichlet non-improvable numbers versus well-approximable numbers
Bo Tan, Qing-Long Zhou
Let be a set that supports a probability measure with the property that for some constant Let $\mathcal{A}=(q_n)_{n\…