Inhomogeneous theory of dual Diophantine approximation on manifolds

TY - JOUR

T1 - Inhomogeneous theory of dual Diophantine approximation on manifolds

AU - Badziahin, Dzmitry

AU - Beresnevich, Victor

AU - Velani, Sanju

N1 - ©2012 Elsevier Inc. This is an author-produced version of the published paper. Uploaded in accordance with the publisher’s self-archiving policy. Further copying may not be permitted; contact the publisher for details

PY - 2013/1/15

Y1 - 2013/1/15

N2 - The theory of inhomogeneous Diophantine approximation on manifolds is developed. In particular, the notion of nice manifolds is introduced and the divergence part of the Groshev type theory is established for all such manifolds. Our results naturally incorporate and generalize the homogeneous measure and dimension theorems for non-degenerate manifolds established to date. The results have natural applications beyond the standard inhomogeneous theory such as Diophantine approximation by algebraic integers.

AB - The theory of inhomogeneous Diophantine approximation on manifolds is developed. In particular, the notion of nice manifolds is introduced and the divergence part of the Groshev type theory is established for all such manifolds. Our results naturally incorporate and generalize the homogeneous measure and dimension theorems for non-degenerate manifolds established to date. The results have natural applications beyond the standard inhomogeneous theory such as Diophantine approximation by algebraic integers.

KW - Diophantine approximation

KW - extremal manifolds

KW - ubiquitous systems

KW - Groshev type theorem

UR - http://www.scopus.com/inward/record.url?scp=84867448296&partnerID=8YFLogxK

U2 - 10.1016/j.aim.2012.09.022

DO - 10.1016/j.aim.2012.09.022

M3 - Article

SN - 0001-8708

VL - 232

SP - 1

EP - 35

JO - Advances in Mathematics

JF - Advances in Mathematics

IS - 1

ER -