Kui Liu

activity

20122022

most citedA variant of the prime number theorem

4 citations · 4 across the 6 of their papers we have counts for

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8 papers · 1 filter

math.NT2022

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

Kui Liu, Meijie Lu, Xianchang Meng

For any integers $k \geq 2$ , $q \geq 1$ and any finite set $A = {α_{1}, \dots, α_{q}}$ , where ${ \boldsymbolα_t}=(α_{t,1},\cdots,α_{t,k})~(1\leq t\leq…

math.NT2022

$k$ -free lattice points in random walks

Kui Liu, Shunqi Ma

Let $Z^{2}$ be the two-dimensional integer lattice. For an integer $k \geq 1$ , a non-zero lattice point is $k$ -free if the greatest common divisor of its coordinates is a $k$ …

math.NT2021

On some sums involving the integral part function

Kui Liu, Jie Wu, Zhishan Yang

Denote by $τ$ k (n), $ω$ (n) and $μ$ 2 (n) the number of representations of n as product of k natural numbers, the number of distinct prime factors of n and the characteristic funct…

math.NT2021★ 4 cited

A variant of the prime number theorem

Kui Liu, Jie Wu, Zhishan Yang

Let $Λ (n)$ be the von Mangoldt function, and let $[t]$ be the integral part of real number $t$ . In this note, we prove that for any $ε > 0$ the asymptotic formula $$ \sum_{…

math.NT2020

Random walks on generalized visible lattice points

Kui Liu, Xianchang Meng

We consider the proportion of generalized visible lattice points in the plane visited by random walkers. Our work concerns the visible lattice points in random walks in three aspec…