Metric Diophantine approximation with congruence conditions
Number Theory
2019-02-06 v2 Dynamical Systems
Abstract
We prove a version of the Khinchine--Groshev theorem for Diophantine approximation of matrices subject to a congruence condition. The proof relies on an extension of the Dani correspondence to the quotient by a congruence subgroup. This correspondence together with a multiple ergodic theorem are used to study rational approximations in several congruence classes simultaneously. The result in this part holds in the generality of weighted approximation but is restricted to simple approximation functions.
Cite
@article{arxiv.1902.01381,
title = {Metric Diophantine approximation with congruence conditions},
author = {Erez Nesharim and Rene Rühr and Ronggang Shi},
journal= {arXiv preprint arXiv:1902.01381},
year = {2019}
}