Central limit theorems in the geometry of numbers
Artikel i vetenskaplig tidskrift, 2017

We investigate in this paper the distribution of the discrepancy of various lattice counting functions. In particular, we prove that the number of lattice points contained in certain domains defined by products of linear forms satisfies a Central Limit Theorem. Furthermore, we show that the Central Limit Theorem holds for the number of rational approximants for weighted Diophantine approximation in ?d. Our arguments exploit chaotic properties of the Cartan flow on the space of lattices.

Diophantine approximation

Central Limit Theorems

Författare

Michael Björklund

Göteborgs universitet

Chalmers, Matematiska vetenskaper, Analys och sannolikhetsteori

Alexander Gorodnik

Electronic Research Announcements in Mathematical Sciences

1935-9179 (ISSN)

Vol. 24 110-122

Ämneskategorier

Matematik

DOI

10.3934/era.2017.24.012