Central limit theorems for Diophantine approximants

DOI10.1007/s00208-019-01828-1zbMath1456.11143arXiv1804.06084OpenAlexW2963495604WikidataQ128005984 ScholiaQ128005984MaRDI QIDQ2314798

Alexander Gorodnik, Michael Björklund

Publication date: 30 July 2019

Published in: Mathematische Annalen (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1804.06084

zbMATH Keywords

homogeneous dynamicscounting functionsSiegel transforms

Mathematics Subject Classification ID

Central limit and other weak theorems (60F05) Diophantine approximation in probabilistic number theory (11K60) Homogeneous flows (37A17)

Related Items (8)

Multiple Borel-Cantelli lemma in dynamics and multilog law for recurrence ⋮ Rogers' mean value theorem for \(S\)-arithmetic Siegel transforms and applications to the geometry of numbers ⋮ A measure estimate in geometry of numbers and improvements to Dirichlet's theorem ⋮ A central limit theorem for counting functions related to symplectic lattices and bounded sets ⋮ Higher Order Correlations for Group Actions ⋮ Central limit theorem and cohomological equation on homogeneous spaces ⋮ Central limit theorems for generic lattice point counting ⋮ Poisson approximation and Weibull asymptotics in the geometry of numbers

Cites Work

• Unnamed Item
• Upper bounds and asymptotics in a quantitative version of the Oppenheim conjecture
• Flows on homogeneous spaces and Diophantine approximation on manifolds
• Invariance principles for diagonal flows on \(SL(d,\mathbb{R})/SL(d,\mathbb{Z})\)
• Central limit theorems for group actions which are exponentially mixing of all orders
• Central limit theorems for simultaneous Diophantine approximations
• Quantitative multiple mixing
• Asymptotic formulae for point lattices of bounded determinant and subspaces of bounded height
• A mean value theorem in geometry of numbers
• Mean values over the space of lattices
• On effective equidistribution of expanding translates of certain orbits in the space of lattices
• On the Frequency of Small Fractional Parts in Certain Real Sequences
• On the Frequency of Small Fractional Parts in Certain Real Sequences. II
• A Metrical Theorem in Diophantine Approximation
• A Proof of the Generalized Second-Limit Theorem in the Theory of Probability
• On a problem of W. J. LeVeque concerning metric diophantine approximation
• Mixing sequences of random variables and probablistic number theory

This page was built for publication: Central limit theorems for Diophantine approximants