Geodesic
On Diophantine Approximations of Dependent Quantities in the $p$-adic Case
Matematičeskie zametki, Tome 73 (2003) no. 1, pp. 22-37.

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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. 
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V. V. Beresnevich; É. I. Kovalevskaya. On Diophantine Approximations of Dependent Quantities in the $p$-adic Case. Matematičeskie zametki, Tome 73 (2003) no. 1, pp. 22-37. http://geodesic.mathdoc.fr/item/MZM_2003_73_1_a2/

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