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JOURNALS // Chebyshevskii Sbornik // Archive

Chebyshevskii Sb., 2011 Volume 12, Issue 4, Pages 43–74 (Mi cheb109)

Regular and ubiquitous systems for simultaneous Diophantine approximations

N. V. Budarina

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

Abstract: In this paper the Khintchine type theorem for polynomials in the divergence case is generalised to simultaneous approximations in $\mathbb{R}^k\times\mathbb{C}^l\times\mathbb{Q}_p^m$ and to approximations which incorporate a natural restriction on derivatives. The proof builds upon the construction of the optimal regular systems, the ubiquity technique and the construction of a system of close conjugate algebraic numbers.

UDC: 511.42, 511.72

MSC: 11J13

Received: 12.12.2011



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