Metric theory of simultaneous Diophantine approximations in $\mathbb{R}^k\times\mathbb{C}^l\times\mathbb{Q}^m_p$
Čebyševskij sbornik, Tome 12 (2011) no. 1, pp. 17-50.

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N. V. Budarina. Metric theory of simultaneous Diophantine approximations in $\mathbb{R}^k\times\mathbb{C}^l\times\mathbb{Q}^m_p$. Čebyševskij sbornik, Tome 12 (2011) no. 1, pp. 17-50. http://geodesic.mathdoc.fr/item/CHEB_2011_12_1_a2/

[1] A. Baker, “On a theorem of Sprindzuk”, Proc. Roy. Soc., London Ser. A, 292 (1966), 92–104 | DOI | Zbl

[2] V. Beresnevich, “On approximation of real numbers by real algebraic numbers”, Acta Arith., 90 (1999), 97–112 | MR | Zbl

[3] V. Beresnevich, “A Groshev type theorem for convergence on manifolds”, Acta Math. Hungar., 94 (2002), 99–130 | DOI | MR | Zbl

[4] V. V. Beresnevich, V. I. Bernik, D. Y. Kleinbock, G. A. Margulis, “Metric Diophantine approximation: the Khintchine–Groshev theorem for nondegenerate manifolds”, Mosc. Math. J., 2 (2002), 203–225 | MR | Zbl

[5] V. Beresnevich, V. Bernik, E. Kovalevskaya, “On approximation of $p$-adic numbers by $p$-adic algebraic numbers”, Journal of Number Theory, 111 (2005), 33–56 | DOI | MR | Zbl

[6] V. Beresnevich, D. Dickinson, S. Velani, “Measure theoretic laws for lim sup sets”, Mem. Amer. Math. Soc., 179, no. 846, 2006, 91 | MR | Zbl

[7] V. Bernik, “The metric theorem on the simultaneous approximation of zero by values of integral polynomials”, Izv. Akad. Nauk SSSR, Ser. Mat., 44 (1980), 24–45 | MR | Zbl

[8] V. Bernik, “On the exact order of approximation of zero by values of integral polynomials”, Acta Arith., 53 (1989), 17–28 | MR | Zbl

[9] V. Bernik, D. Vasilyev, “A Khinchin-type theorem for integral-valued polynomials of a complex variable”, Proc. IM NAN Belarus, 3 (1999), 10–20 | MR | Zbl

[10] V. I. Bernik, D. Kleinbock, G. A. Margulis, “Khintchine-type theorems on manifolds: the convergence case for standard and multiplicative versions”, Internat. Math. Res. Notices, 2001, no. 9, 453–486 | DOI | MR | Zbl

[11] V. Bernik, N. Kalosha, “Approximation of zero by values of integral polynomials in space $\mathbb R\times\mathbb C\times\mathbb Q_p$”, Vesti NAN of Belarus. Ser. fiz-mat nauk, 2004, no. 1, 121–123 | MR

[12] V. Bernik, N. Shamukova, “Approximation of real numbers by integer algebraic numbers, and the Khinchin theorem”, Dokl. Nats. Akad. Nauk Belarusi, 50:3 (2006), 30–32 | MR | Zbl

[13] Y. Bugeaud, “Approximation by algebraic integers and Hausdorff dimension”, J. Lond. Math. Soc., 65:3 (2002), 547–559 | DOI | MR | Zbl

[14] A. Khintchine, “Einige Sa̋tze uber Kettenbrűche mit Anwendungen auf die Theorie der Diophantischen Approximationen”, Math. Ann., 92 (1924), 115–125 | DOI | MR | Zbl

[15] E. Kovalevskaya, On the exact order of approximation to zero by values of integral polynomials in $\mathbb Q_p$, Preprint Institute Math. National Academy Sciences Belarus No 8(547), Minsk, 1998

[16] K. Mahler, “Über das Mass der Menge aller $S$–Zahlen”, Math.Ann., 106 (1932), 131–139 | DOI | MR

[17] V. Sprindzuk, Mahler's problem in the Metric Theory of Numbers, Transl. Math. Monographs, 25, Amer. Math. Soc., Providence, R.I., 1969 | MR

[18] F. Z̋eludevich, “Simultane diophantishe Approximationen abhangiger Grössen in mehreren Metriken”, Acta Arith., 46 (1986), 285–296 | MR