Central limit theorems for Diophantine approximants
Journal article, 2019

© 2019, The Author(s). 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.

Author

Michael Björklund

Chalmers, Mathematical Sciences, Analysis and Probability Theory

Alexander Gorodnik

University of Zürich

Mathematische Annalen

0025-5831 (ISSN) 1432-1807 (eISSN)

Vol. 374 3-4 1371-1437

Subject Categories

Computational Mathematics

Probability Theory and Statistics

Mathematical Analysis

DOI

10.1007/s00208-019-01828-1

More information

Latest update

4/6/2022 5