Simultaneous inhomogeneous Diophantine approximation of the values of integral polynomials with respect to Archimedean and non-Archimedean valuations

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1. Baker A., On a theorem of Sprindz̆uk, , Proc. Roy. Soc. London Ser. A 242 (1966), 92-104. (1966) 
2. Beresnevich V., Bernik V., Kleinbock D., Margulies G.A., Metric Diophantine approximation: the Khintchine-Groshev theorem for non-degenerate ma nifolds, , Moscow Math. J. 2 (2002), 203-225. MR1944505
3. Beresnevich V.V., Bernik V.I., Kovalevskaya E.I., 10.1016/j.jnt.2004.09.007, , J. Number Theory 111 (2005), 33-56. Zbl1078.11050MR2124042DOI10.1016/j.jnt.2004.09.007
4. Bernik V.I., Borbat V.N., Simultaneous approximation of zero values of integral polynomials in ${\mathbb{Q}}_p$, , Proc. of the Steklov Institute of Math. 218 (1997), 53-68 (translated by S.Varhromeev/MAHK Hayka /Interperiodica Publishing (Russia)). (1997) MR1642345
5. Bernik V.I., Dickinson H., Dodson M., Approximation of real numbers by integral polynomials, , Dokl. Nats. Akad. Nayk Belarusi 42 (1997), 51-54. (1997) 
6. Bernik V., Dickinson H., Yuan J., Inhomogeneous diohantine approximation on polynomials, , Acta Arith. 90 (1999), 37-48. (1999) MR1708696
7. Bernik V.I., Dodson M.M., Metric Diophantine approximation on manifolds, . Cambridge Tracts in Math. Vol. 137. Cambridge Univ. Press, 1999. (1999) Zbl0933.11040MR1727177
8. Bernik V.I., Kalosha N.I., Simultaneous approximation of zero values of integral polynomials in $ℝ\times {\mathbb{Q}}_p$, , Dokl. Nats. Akad. Nauk Belarusi. 47 (2003), 19-22. MR2163815
9. Bernik V., Kleinbock D., Margulies G.A., 10.1155/S1073792801000241, , Int. Math. Research Notices. 9 (2001), 453-486. MR1829381DOI10.1155/S1073792801000241
10. Bugeaud Y., Approximation by algebraic numbers, . Cambridge Tracts in Math. 169, Cambridge Univ. Press, Cambridge, 2004. Zbl1155.11003MR2136100
11. Giong, Pan., Metric inhomogeneous Diophantine approximation on polynomial curves in ${\mathbb{Q}}_p$ (to appear), . 
12. Harman G., Metric Number Theory, . LMS Monograph. New Series. Vol. 18. Claredon Press, 1998. (1998) Zbl1081.11057MR1672558
13. Kleinbock D., Margulies G.A., 10.2307/120997, , Ann. Math. 148 (1998), 339-360. (1998) MR1652916DOI10.2307/120997
14. Kleinbock D., Tomanov G., Flows on $S$-arithmetic homogeneous space and application to metric Diophantine approximation, , Preprint Max Plank Institute. Bonn. 2003-65 (2003). MR2314053
15. Kovalevskaya E.I., A metric theorem on the exact order of approximation of zero by values of integral polynomials in ${\mathbb{Q}}_p$, , Dokl. Nats. Akad. Nauk Belarusi. 43 (1999), 34-36. (1999) MR1741903
16. Kovalevskaya E., Simultaneous approximation of zero by values of integral polynomials with respect to different valuations, , Math. Slovaca. 54 (2004), 479-486. Zbl1108.11050MR2114619
17. Schmidt W.M., Diophantine Approximation, . Lecture Notes in Math. Vol. 785. Springer-Verlag, 1980. (1980) Zbl0421.10019MR0568710
18. Sprindz̆uk V.G., Mahler’s problem in metric Number Theory, , Nauka i Tehnika, Minsk, 1967 [Transl. Math. Monogr. 25, Amer. Math. Soc., Providence, R.I., 1969]. (Russian) (1967) MR0245526
19. Sprindz̆uk V.G., Metric Theory of Diophantine Approximation, , Izdatel’stvo Nauka, Mos-kva, 1977 [Jihn Wiley, New York-Toronto-London, 1979 (translation by R. A. Silverman)]. (Russian) (1977) MR0548467
20. Z̆eludevich F., Simultine diophantishe Approximationen abha̋ngiger Grőssen in mehreren Metriken, , Acta Arithm. 46 (1986), 285-296. (1986) 
21. Ustinov A. E., Inhomogeneous approximation on manifolds in ${\mathbb{Q}}_p$, , Vestsi Nats. Akad. Nauk Belarusi. Ser. fiz.-mat. nauk. No 3 (2005), 30-34 MR2210400
22. Ustinov A. E., Inhomogeneous approximation on manifolds in $ℂ`$, , Vestsi Nats. Akad. Nauk Belarusi. Ser. fiz.-mat. nauk. No 1 (2006), 9-14. MR2229813