This article is cited in 12 papers

On Diophantine Approximations of Dependent Quantities in the $p$-adic Case

V. V. Beresnevich, É. I. Kovalevskaya

Institute of Mathematics, National Academy of Sciences of the Republic of Belarus

Abstract: In the present paper, we prove an analog of Khinchin's metric theorem in the case of linear Diophantine approximations of plane curves defined over the ring of $p$-adic integers by means of (Mahler) normal functions. We also prove some general assertions needed to generalize this result to the case of spaces of higher dimension.

UDC: 511.36

Received: 20.10.2000

DOI: 10.4213/mzm165

 English version: Mathematical Notes, 2003, 73:1, 21–35

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