Geodesic
Regular and ubiquitous systems for simultaneous Diophantine approximations
Čebyševskij sbornik, Tome 12 (2011) no. 4, pp. 43-74

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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. 
@article{CHEB_2011_12_4_a5,
     author = {N. V. Budarina},
     title = {Regular and ubiquitous systems for simultaneous {Diophantine} approximations},
     journal = {\v{C}eby\v{s}evskij sbornik},
     pages = {43--74},
     publisher = {mathdoc},
     volume = {12},
     number = {4},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/CHEB_2011_12_4_a5/}
}
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N. V. Budarina. Regular and ubiquitous systems for simultaneous Diophantine approximations. Čebyševskij sbornik, Tome 12 (2011) no. 4, pp. 43-74. http://geodesic.mathdoc.fr/item/CHEB_2011_12_4_a5/