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Dal'nevost. Mat. Zh., 2013, Volume 13, Number 2, Pages 164–178 (Mi dvmg260)  

Inhomogeneous Diophantine approximation on curves with non-monotonic error function

N. V. Budarina

Institute for Applied Mathematics, Khabarovsk Division, Far-Eastern Branch of the Russian Academy of Sciences

Abstract: In this paper we prove a convergent part of inhomogeneous Groshev type theorem for non–degenerate curves in Euclidean space where an error function is not necessarily monotonic. Our result naturally incorporates and generalizes the homogeneous measure theorem for non-degenerate curves. In particular, the method of Inhomogeneous Transference Principle and Sprindzuk's method of essential and inessential domains are used in the proof.

Key words: Inhomogeneous Diophantine approximation, Khintchine theorem, nondegenerate curve

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UDC: 511.42
MSC: 11K60
Received: 24.08.2013
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Citation: N. V. Budarina, “Inhomogeneous Diophantine approximation on curves with non-monotonic error function”, Dal'nevost. Mat. Zh., 13:2 (2013), 164–178

Citation in format AMSBIB
\Bibitem{Bud13}
\by N.~V.~Budarina
\paper Inhomogeneous Diophantine approximation on curves with non-monotonic error function
\jour Dal'nevost. Mat. Zh.
\yr 2013
\vol 13
\issue 2
\pages 164--178
\mathnet{http://mi.mathnet.ru/dvmg260}


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