Výsledky vyhledávání

Report

On the distribution of $k$-free numbers on the view point of random walks

Autor: Liu, Kui, Lu, Meijie

In this paper, we investigate the distribution of $k$-free numbers in a class of $\alpha$-random walks on the integer lattice $\mathbb{Z}$. In these walks, the walker starts from a non-negative integer $r$ and moves to the right by $a$ units with pro

Externí odkaz: http://arxiv.org/abs/2309.06210

Zobrazit plný text záznamu

Report

Visible lattice points in P\'{o}lya's walk

Autor: Lu, Meijie, Meng, Xianchang

In this paper, for any integer $k\geq 2$, we study the distribution of the visible lattice points in certain generalized P\'{o}lya's walk on $\mathbb{Z}^k$: perturbed P\'{o}lya's walk and twisted P\'{o}lya's walk. For the first case, we prove that th

Externí odkaz: http://arxiv.org/abs/2307.16583

Zobrazit plný text záznamu

Report

Visible lattice points in higher dimensional random walks and biases among them

Autor: Liu, Kui, Lu, Meijie, Meng, Xianchang

For any integers $k\geq 2$, $q\geq 1$ and any finite set $\mathcal{A}=\{{\boldsymbol{\alpha}}_1,\cdots,{\boldsymbol{\alpha}}_q\}$, where ${ \boldsymbol{\alpha}_t}=(\alpha_{t,1},\cdots,\alpha_{t,k})~(1\leq t\leq q)$ with $0<\alpha_{t,1},\cdots,\alpha_

Externí odkaz: http://arxiv.org/abs/2210.07464

Zobrazit plný text záznamu