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Metric Diophantine approximation with congruence conditions by Nesharim, Erez; Rühr, Rene; Shi, Ronggang is a scholarly article available to read on EtoBox.

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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.

Author

Nesharim, Erez; Rühr, Rene; Shi, Ronggang

Published

2019

Language

EN