Geodesic
$P$-adic Diophantine approximation on the Veronese curve with a non-monotonic error
Trudy Instituta matematiki, Tome 15 (2007) no. 1, pp. 98-104

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A $p$-adic analogue of the convergence part of Khintchine's Theorem for polynomials is proved with a non-monotonic error function. This is a small strengthening of Sprindžuk's theorem and a generalization of a result of Beresnevich. 
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     title = {$P$-adic {Diophantine} approximation on the {Veronese} curve with a non-monotonic error},
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N. V. Budarina; D. Dickinson. $P$-adic Diophantine approximation on the Veronese curve with a non-monotonic error. Trudy Instituta matematiki, Tome 15 (2007) no. 1, pp. 98-104. http://geodesic.mathdoc.fr/item/TIMB_2007_15_1_a10/