Central Limit Theorems in Multiplicative Diophantine Approximation
Number Theory
2026-01-21 v1 Dynamical Systems
Probability
Abstract
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 normal law. Our approach relies on the analysis of correlations of measures on homogeneous spaces, together with estimates for Siegel transforms restricted to subspaces.
Cite
@article{arxiv.2601.13726,
title = {Central Limit Theorems in Multiplicative Diophantine Approximation},
author = {Michael Björklund and Reynold Fregoli and Alexander Gorodnik},
journal= {arXiv preprint arXiv:2601.13726},
year = {2026}
}
Comments
42 pages, comments are welcome!