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Dal'nevostochnyi Matematicheskii Zhurnal, 2013, Volume 13, Number 2, Pages 164–178
(Mi dvmg260)
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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.
Received: 24.08.2013
Citation:
N. V. Budarina, “Inhomogeneous Diophantine approximation on curves with non-monotonic error function”, Dal'nevost. Mat. Zh., 13:2 (2013), 164–178
Linking options:
https://www.mathnet.ru/eng/dvmg260 https://www.mathnet.ru/eng/dvmg/v13/i2/p164
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Abstract page: | 202 | Full-text PDF : | 70 | References: | 41 | First page: | 1 |
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