Central Limit Theorems in Multiplicative Diophantine Approximation
arXiv:2601.13726
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.
42 pages, comments are welcome!