Publication: Central limit theorems for Diophantine approximants
Central limit theorems for Diophantine approximants
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Björklund, M., & Gorodnik, A. (2019). Central limit theorems for Diophantine approximants. Mathematische Annalen, 374(3–4), 1371–1437. https://doi.org/10.1007/s00208-019-01828-1
Abstract
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Abstract
In this paper we study certain counting functions which represent the numbers of solutions of systems of linear inequalities arising in the theory of Diophantine approximation. We develop a method that allows us to explain the random-like behavior that these functions exhibit and prove a central limit theorem for them. Our approach is based on a quantitative study of higher-order correlations for functions defined on the space of lattices and a novel technique for estimating cumulants of Siegel transforms.
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- Björklund, Michael
- Gorodnik, Alexander
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Citations
Björklund, M., & Gorodnik, A. (2019). Central limit theorems for Diophantine approximants. Mathematische Annalen, 374(3–4), 1371–1437. https://doi.org/10.1007/s00208-019-01828-1
