Research PaperNo Access

Metric Diophantine approximation with congruence conditions

Erez Nesharim

Faculty of Mathematics, Technion, Haifa 3200003, Israel

E-mail Address: [email protected]

Corresponding author.

Present address: Einstein Institute of Mathematics, The Hebrew University of Jerusalem, Jerusalem 9190401, Israel.

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René Rühr

Faculty of Mathematics, Technion, Haifa 3200003, Israel

E-mail Address: [email protected]

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, and

Ronggang Shi

Shanghai Center for Mathematical Sciences, Fudan University, Shanghai 200433, P. R. China

E-mail Address: [email protected]

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https://doi.org/10.1142/S1793042120500980Cited by:2 (Source: Crossref)

Abstract

We prove a version of the Khinchin–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.

Keywords:

AMSC: 11J13, 11J83

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