Runlin Zhang

activity

20182026

most citedEquidistribution of translates of a homogeneous measure on the Borel--Serre boundary

3 citations · 3 across the 11 of their papers we have counts for

collaborators

11 papers

math.NT2026

Effective count of integer points on ternary affine quadrics and effective equidistribution

Runlin Zhang

We study the effective equidistribution of certain infinite homogeneous measures and related counting problems through mixing. In this way, we obtain smooth versions of counting th…

math.NT2025

Effective equidistribution, arithmetic purity of strong approximation, and geometric sieve for affine quadrics

Yang Cao, Zhizhong Huang, Runlin Zhang

Let $k$ be a number field. Let $q (x_{1}, \dots, x_{n})$ be a non-degenerate integral quadratic form in $n \geq 3$ variables with coefficients in $k$ and $m \in k^{\times}$ . Let $X$ be the a…

math.DS2024

Asymptotics of integral points, equivariant compactifications and equidistributions for homogeneous spaces

Runlin Zhang

Let U be a homogeneous variety over Q of a linear algebraic group. Choose an integral model and assume the existence of infinitely many integral points. Then one would like to give…

math.DS2022

Nondivergence of Reductive group action on Homogeneous Spaces

Han Zhang, Runlin Zhang

Let $X = G /Γ$ be the quotient of a semisimple Lie group $G$ by its non-cocompact arithmetic lattice. Let $H$ be a reductive algebraic subgroup of $G$ acting on $X$ . We give several e…

math.DS2021

Count lifts of non-maximal closed horocycles on $S L_{N} (Z) \ S L_{N} (R) / S O_{N} (R)$

Runlin Zhang

A closed horocycle $U$ on $S L_{N} (Z) \ S L_{N} (R) / S O_{N} (R)$ has many lifts to the universal cover $S L_{N} (R) / S O_{N} (R)$ . U…

math.DS2021

Nondivergence on homogeneous spaces and rigid totally geodesics

Han Zhang, Runlin Zhang

Let $G /Γ$ be the quotient of a semisimple Lie group by an arithmetic lattice. We show that for reductive subgroups $H$ of $G$ that is large enough, the orbits of $H$ on $G /Γ$ inter…

math.NT2021

Counting integral points on indefinite ternary quadratic equations over number fields

Fei Xu, Runlin Zhang

We study an asymptotic formula for counting integral points over an equation defined by a non-degenerated indefinite integral ternary quadratic form $f$ representing a non-zero int…

math.DS2021★ 3 cited

Equidistribution of translates of a homogeneous measure on the Borel--Serre boundary

Runlin Zhang

Let G be a semisimple linear algebraic group defined over rational numbers, K be a maximal compact subgroup of its real points and Γ be an arithmetic lattice. One can associate a p…

math.NT2021

Counting integral points on some homogeneous varieties with large reductive stabilizers

Runlin Zhang

Let G be a semisimple group over rational numbers and H is a subgroup over rational numbers. Given a representation of G and an integral vector x whose stabilizer is equal to H. In…

math.DS2019

Translates of homogeneous measures associated with observable subgroups on some homogeneous spaces

Runlin Zhang

In the present article we study the following problem. Let G be a linear algebraic group over Q, $Γ$ be an arithmetic lattice and H be an observable Q-subgroup. There is a H-invari…

math.DS2018

Limiting distribution of translates of the orbit of a maximal $Q$ -torus from identity on $S L (N, R) / S L (N, Z)$

Runlin Zhang

Given a maximal $Q$ -torus in $S L (N, Q)$ , its orbit from identity coset in $S L (N, R) / S L (N, Z)$ naturally carries a possibly infinite Haar measure. W…

Effective count of integer points on ternary affine quadrics and effective equidistribution

Effective equidistribution, arithmetic purity of strong approximation, and geometric sieve for affine quadrics

Asymptotics of integral points, equivariant compactifications and equidistributions for homogeneous spaces

Nondivergence of Reductive group action on Homogeneous Spaces

Count lifts of non-maximal closed horocycles on SLN​(Z)\SLN​(R)/SON​(R)

Nondivergence on homogeneous spaces and rigid totally geodesics

Counting integral points on indefinite ternary quadratic equations over number fields

Equidistribution of translates of a homogeneous measure on the Borel--Serre boundary

Counting integral points on some homogeneous varieties with large reductive stabilizers

Translates of homogeneous measures associated with observable subgroups on some homogeneous spaces

Limiting distribution of translates of the orbit of a maximal Q-torus from identity on SL(N,R)/SL(N,Z)

Count lifts of non-maximal closed horocycles on $S L_{N} (Z) \ S L_{N} (R) / S O_{N} (R)$

Limiting distribution of translates of the orbit of a maximal $Q$ -torus from identity on $S L (N, R) / S L (N, Z)$