6 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 -weight…
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…
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…
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 …