Zobrazeno 1 - 10
of 51
pro vyhledávání: '"Meng, Xianchang"'
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
Autor:
Lu, Zhipeng, Meng, Xianchang
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-Sharir framework. In short words, they study the second moment in the fram
Externí odkaz:
http://arxiv.org/abs/2211.12682
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
Autor:
Liu, Kui, Meng, Xianchang
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 aspects: (1) generalized visibility along curves; (2) one random walker vis
Externí odkaz:
http://arxiv.org/abs/2009.03609
Autor:
Meng, Xianchang
For any cofinite Fuchsian group $\Gamma\subset {\rm PSL}(2, \mathbb{R})$, we show that any set of $N$ points on the hyperbolic surface $\Gamma\backslash\mathbb{H}^2$ determines $\geq C_{\Gamma} \frac{N}{\log N}$ distinct distances for some constant $
Externí odkaz:
http://arxiv.org/abs/2008.01678
Autor:
Lu, Zhipeng, Meng, Xianchang
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 representatives realizing distances in the corresponding hyperbolic surface. Then w
Externí odkaz:
http://arxiv.org/abs/2006.16565
Autor:
Liu, Kui, Meng, Xianchang
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 the concept of level of visibility, we are able to analyze more carefull
Externí odkaz:
http://arxiv.org/abs/2005.13994
Autor:
Devin, Lucile, Meng, Xianchang
Publikováno v:
Advances in Mathematics Volume 392, 3 December 2021, 108040
For any $k\geq 1$, this paper studies the number of polynomials having $k$ irreducible factors (counted with or without multiplicities) in $\mathbf{F}_q[t]$ among different arithmetic progressions. We obtain asymptotic formulas for the difference of
Externí odkaz:
http://arxiv.org/abs/1809.09662
Autor:
Meng, Xianchang
We consider the summatory function of the number of prime factors for integers $\leq x$ over arithmetic progressions. Numerical experiments suggest that some arithmetic progressions consist more number of prime factors than others. Greg Martin conjec
Externí odkaz:
http://arxiv.org/abs/1801.06906
Publikováno v:
In Journal of Number Theory December 2022 241:314-329
