Xianchang Meng

activity

20142023

most citedChebyshev's bias for products of irreducible polynomials

10 citations · 29 across the 14 of their papers we have counts for

collaborators

14 papers

math.NT2023★ 1 cited

Visible lattice points in Pólya's walk

Meijie Lu, Xianchang Meng

In this paper, for any integer $k \geq 2$ , we study the distribution of the visible lattice points in certain generalized Pólya's walk on $Z^{k}$ : perturbed Pólya's walk and…

math.CO2022

Asymptotic estimate on the distance energy of lattices

Zhipeng Lu, Xianchang Meng

Since the well-known breakthrough of L. Guth and N. Katz on the Erdos distinct distances problem in the plane, mainstream of interest is aroused by their method and the Elekes-Shar…

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.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…

math.NT2020★ 1 cited

Distinct distances on hyperbolic surfaces

Xianchang Meng

For any cofinite Fuchsian group $Γ \subset PSL (2, R)$ , we show that any set of $N$ points on the hyperbolic surface $Γ\ H^{2}$ determines $\geq C_Γ \fr…

math.NT2020★ 2 cited

Erdős distinct distances in hyperbolic surfaces

Zhipeng Lu, Xianchang Meng

In this paper, we introduce the notion of "geodesic cover" for Fuchsian groups, which summons copies of fundamental polygons in the hyperbolic plane to cover pairs of representativ…

math.NT2020

Visible lattice points along curves

Kui Liu, Xianchang Meng

This paper concerns the number of lattice points in the plane which are visible along certain curves to all elements in some set S of lattice points simultaneously. By proposing th…

math.NT2018★ 10 cited

Chebyshev's bias for products of irreducible polynomials

Lucile Devin, Xianchang Meng

For any $k \geq 1$ , this paper studies the number of polynomials having $k$ irreducible factors (counted with or without multiplicities) in $F_{q} [t]$ among different arithme…

math.NT2018

Summatory function of the number of prime factors

Xianchang Meng

We consider the summatory function of the number of prime factors for integers $\leq x$ over arithmetic progressions. Numerical experiments suggest that some arithmetic progression…

math.NT2017★ 1 cited

Discrete bilinear Radon transforms along arithmetic functions with many common values

Dong Dong, Xianchang Meng

We prove that for a large class of functions $P$ and $Q$ , there exists $d \in (0, 1)$ such that the discrete bilinear Radon transform $$B^{\rm dis}_{P,Q}(f,g)(n)=\sum_{m\in\mathbb{Z}…

math.NT2016★ 5 cited

Large bias for integers with prime factors in arithmetic progressions

Xianchang Meng

We prove an asymptotic formula for the number of integers $\leq x$ which can be written as the product of $k (\geq 2)$ distinct primes $p_{1} \dots p_{k}$ with each prime factor in an…

math.NT2016★ 6 cited

Chebyshev's bias for products of $k$ primes

Xianchang Meng

For any $k \geq 1$ , we study the distribution of the difference between the number of integers $n \leq x$ with $ω (n) = k$ or $Ω (n) = k$ in two different arithmetic progressions, where $ω…

math.NT2015★ 2 cited

Simultaneous distribution of fractional parts of Riemann zeta zeros

Kevin Ford, Xianchang Meng, Alexandru Zaharescu

We investigate the simultaneous distribution of the fractional parts of ${α_{1} γ, α_{2} γ, \dots, α_{n} γ}$ , where $n \geq 2$ , $α_{1}$ , $α_{2}$ , $\dots$ , $α_{n}$ are fixed, distinct positive…

math.NT2014★ 1 cited

The distribution of $k$ -free numbers and the derivative of the Riemann zeta-function

Xianchang Meng

Under the Riemann Hypothesis, we connect the distribution of $k$ -free numbers with the derivative of the Riemann zeta-function at nontrivial zeros of $ζ (s)$ . Moreover, with additio…

Visible lattice points in Pólya's walk

Asymptotic estimate on the distance energy of lattices

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

Random walks on generalized visible lattice points

Distinct distances on hyperbolic surfaces

Erdős distinct distances in hyperbolic surfaces

Visible lattice points along curves

Chebyshev's bias for products of irreducible polynomials

Summatory function of the number of prime factors

Discrete bilinear Radon transforms along arithmetic functions with many common values

Large bias for integers with prime factors in arithmetic progressions

Chebyshev's bias for products of k primes

Simultaneous distribution of fractional parts of Riemann zeta zeros

The distribution of k-free numbers and the derivative of the Riemann zeta-function

Chebyshev's bias for products of $k$ primes

The distribution of $k$ -free numbers and the derivative of the Riemann zeta-function