2 citations · 2 across the 13 of their papers we have counts for
15 papers
Central Limit Theorems in Multiplicative Diophantine Approximation
Michael Björklund, Reynold Fregoli, Alexander Gorodnik
We investigate the number of integer solutions to a multiplicative Diophantine approximation problem and show that the associated counting function converges in distribution to a n…
On the Hausdorff Dimension of weighted exactly Approximable Vectors
Prasuna Bandi, Reynold Fregoli
We show that the Hausdorff dimension of -weighted -exactly approximable vectors in coincides with the Hausdorff dimension of -weighte…
Higher-Dimensional Moving Averages and Submanifold Genericity
Jiajun Cheng, Reynold Fregoli, Beinuo Guo
We generalize results of Jones and Olsen on multi-parameter moving ergodic averages to measure-preserving actions of for . In particular, we give necessary a…
Submanifold-genericity of -actions and uniform multiplicative Diophantine approximation
Prasuna Bandi, Reynold Fregoli, Dmitry Kleinbock
In this paper, we prove a new ergodic theorem for -actions involving averages over dilated submanifolds, thereby generalizing the theory of spherical averages. Our ma…
Decorrelation estimates for translated measures under diagonal flows
Michael Björklund, Reynold Fregoli, Alexander Gorodnik
A profound link between Homogeneous Dynamics and Diophantine Approximation is based on an observation that Diophantine properties of a real matrix are encoded by the correspond…
Sums of Reciprocals of Fractional Parts II
Reynold Fregoli
We prove an estimate for the number of lattice points lying in certain non-convex Euclidean domains of interest in Diophantine approximation. As an application, we generalise a res…
A Remark on the Set of Exactly Approximable Vectors in the Simultaneous Case
Reynold Fregoli
We compute the Hausdorff dimension of the set of -exactly approximable vectors, in the simultaneous case, in dimension strictly larger than and for approximating functions $…
On Multiplicatively Badly Approximable Vectors
Reynold Fregoli, Dmitry Kleinbock
Let denote the distance from to the set of integers . The Littlewood Conjecture states that for all pairs t…
A shrinking-target problem in the space of unimodular lattices in the three dimensional Euclidean space
Reynold Fregoli, Cheng Zheng
In this paper, we study the shrinking-target problem with target at infinity induced by the injectivity radius function under the action of a regular diagonalizable flow on $\opera…
A uniform metrical theorem in multiplicative Diophantine approximation
Michael Björklund, Reynold Fregoli, Alexander Gorodnik
For Lebesgue generic , we investigate the distribution of small values of products with , where $\|\cdot…
Sums of Reciprocals of Fractional Parts over Aligned Boxes
Reynold Fregoli
In this paper, we prove new upper bounds for sums of reciprocals of fractional parts over general aligned boxes, thus extending a previous result of the author concerning bounds fo…
Multiplicatively badly approximable matrices up to logarithmic factors
Reynold Fregoli
Let denote the distance from to the nearest integer. In this paper, we prove an existence and density statement for matrices $\boldsymbol{A}\in\mathbb{R}^{…
A note on bounded exponential sums
Reynold Fregoli
Let , , and for let . We set $$S_{A}(α,N):=\sum_{\substack{n\in A\n\leq N}}e(nα).$$ Recently, Lambert A'Campo propos…
On a counting theorem for weakly admissible lattices
Reynold Fregoli
We give a precise estimate for the number of lattice points in certain bounded subsets of that involve `hyperbolic spikes' and occur naturally in multiplicative Di…
Sums of reciprocals of fractional parts
Reynold Fregoli
Let and . We consider the sum $\sum_{\boldsymbol{q}\in [-Q,Q]^N\cap\mathbb{Z}^N\backslash\{\boldsymbol{0}\}}\|\boldsymbolα\cdot\boldsymbol{q…