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arXiv · 2601.13726

Central Limit Theorems in Multiplicative Diophantine Approximation

Michael Björklund·Reynold Fregoli·Alexander Gorodnik
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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.

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Michael Björklund, Reynold Fregoli, Alexander Gorodnik. 2026-01-20. Central Limit Theorems in Multiplicative Diophantine Approximation. https://arxiv.org/abs/2601.13726

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