相关论文: Effective joint equidistribution of primitive rati…
We prove an effective version of a result due to Einsiedler, Mozes, Shah and Shapira on the asymptotic distribution of primitive rational points on expanding closed horospheres in the space of lattices. Key ingredients of our proof include…
Einsiedler, Mozes, Shah and Shapira [Compos. Math. 152 (2016), 667-692] prove an equidistribution theorem for rational points on expanding horospheres in the space of d-dimensional Euclidean lattices, with d>2. Their proof exploits measure…
In recent work by Einsiedler, Mozes, Shah and Shapira the limiting distributions of primitive rational points on expanding horospheres was examined in arbitrary dimension, and a suspended version of this result was announced. Motivated by…
We confirm a conjecture of Jens Marklof regarding the equidistribution of certain sparse collections of points on expanding horospheres. These collections are obtained by intersecting the expanded horosphere with a certain manifold of…
In this paper we prove an effective equidistribution result for both primitive and non-primitive points on certain expanding horocycle sections in ASL$(2,\mathbb{Z}) \backslash $ASL$(2,\mathbb{R})$. This provides an effective version of a…
We prove effective equidistribution of primitive rational points and of primitive rational points defined by monomials along long horocycle orbits in products of the torus and the modular surface. This answers a question posed in joint work…
Recently Mohammadi and Salehi-Golsefidy gave necessary and sufficient conditions under which certain translates of homogeneous measures converge, and they determined the limiting measures in the cases of convergence. The class of measures…
We use spectral method to prove a joint equidistribution of primitive rational points and the same along expanding horocycle orbits in the products of the circle and the unit cotangent bundle of the modular surface. This result explicates…
We study the limiting distribution of the rational points under a horizontal translation along a sequence of expanding closed horocycles on the modular surface. Using spectral methods we confirm equidistribution of these sample points for…
We prove bounds for twisted ergodic averages for horocycle flows of hyperbolic surfaces, both in the compact and in the non-compact finite area case. From these bounds we derive effective equidistribution results for horocycle maps. As an…
This paper introduces an abstract spectral approach to prove effective equidistribution of expanding horospheres in hyperbolic manifolds. The method, which is motivated by the approach to counting developed by (Lax-Phillips 1982), produces…
Let $\Gamma$ be a lattice in $G=\mathrm{SL}(2,\mathbb{C})$. We give an effective equidistribution result with precise error terms for expanding translates of pieces of horospherical orbits in $\Gamma\backslash G$. Our method of proof relies…
We prove an effective equidistribution theorem for orbits of certain unipotent subgroups in arithmetic quotients of perfect Lie groups with a polynomial error term. Even for semisimple quotients, our result provides the first infinite…
We prove asymptotic equidistribution results for pieces of large closed horospheres in cofinite hyperbolic manifolds of arbitrary dimension. This extends earlier results by Hejhal and Str\"ombergsson in dimension 2. Our proofs use spectral…
We use a dictionary between lattice point counting inside dilated d-dimensional ellipsoids (Euclidean counting) and counting of lifts of a closed horosphere that intersect a ball of increasing radius, to obtain two types of results.…
It was recently shown by Aka, Einsiedler and Shapira that if d>2, the set of primitive vectors on large spheres when projected to the d-1-dimensional sphere coupled with the shape of the lattice in their orthogonal complement equidistribute…
In this note we prove a joint equidistribution result for discrete low lying horocycles. This generalizes previous work of Blomer and Michel, where it was crucially assumed that the number of discrete points is prime.
In this paper we prove a sparse equidistribution theorem for Gross points over the rational function field $\mathbb{F}_q(t)$. We apply this result to study the reduction map from CM Drinfeld modules to supersingular Drinfeld modules. Our…
We record an alternative proof of a recent joint equidistribution result of Blomer and Michel, based on Ratner's topological rigidity theorem. This approach has the advantage of extending to non-uniform lattices.
We establish the limiting distribution of certain subsets of Farey sequences, i.e., sequences of primitive rational points, on expanding horospheres in covers $\Delta\backslash\mathrm{SL}(n+1,\mathbb{R})$ of…