Central limit theorems for Diophantine approximants
Artikel i vetenskaplig tidskrift, 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.

Författare

Michael Björklund

Chalmers, Matematiska vetenskaper, Analys och sannolikhetsteori

Alexander Gorodnik

Universität Zürich

Mathematische Annalen

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

Ämneskategorier

Beräkningsmatematik

Sannolikhetsteori och statistik

Matematisk analys

DOI

10.1007/s00208-019-01828-1

Mer information

Senast uppdaterat

2019-06-24