Bohan Yang

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math.NT2026

Slowly Divergent Trajectories for Weighted Singular Vectors in R^2

Bohan Yang

Let $w = (w_{1}, w_{2})$ satisfy $w_{1} > w_{2} > 0$ and $w_{1} + w_{2} = 1$ . For every function $f : [0, \infty) \to (0, \infty)$ with $f (t) \to 0$ , we prove that the set of $w$ -singular vectors whose weighted…

math.NT2026

Maximal Gaps for Dilated Lacunary Integer Sequences

Yuval Peres, Bohan Yang

Let $(a_n)_{n\ge1}\subset\mathbb{N}$ be a lacunary sequence, $a_{n+1}\ge q a_n$ for $q>1$. For $x\in\mathbb{T}$, we study the maximal empty circular gap $G_N(x)$ of the f…