The Convergence Part of a Knintchine-Type Theorem in the Ring of Adeles

[1] BERNIK, V. I.: Simultaneous approximation of zero by integer polynomials, Izv. Academy Sci. SSSR. Ser. Math. 44 (1980), 24-45.Search in Google Scholar

[2] BUDARINA, N.-DICKINSON, D.- BERNIK, V.: Simultaneous Diophantine approximation in the real, complex and p-adic fields, Math. Proc. Cambridge Phil. Soc. 149 (2010), 193-216.10.1017/S0305004110000162Search in Google Scholar

[3] BERNIK, V. I.-KALOSHA, N. I.: Approximation of zero by integer polynomials in space R×C×Qp, Proc. National Academy Sci. Belarus. Phis. and Math. Ser. 1 (2004), 121-123.Search in Google Scholar

[4] BERESNEVICH, V. V.-BERNIK, V. I.-KOVALEVSKAYA, E. I.: On approximation of p-adic numbers by p-adic algebraic numbers, J. Number Theory 111 (2005), 3-56.10.1016/j.jnt.2004.09.007Search in Google Scholar

[5] KOVALEVSKAYA, E.: Diophantine approximation in C×Qp,: in: Analytic and Probab. Methods in Number Theory (A. Laurinčikas et al., eds.), Proc. of the 4^th Intern. Conf. in Honour of J. Kubilius, Palanga, Lithuania, 2006, TEV, Vilnius, 2007, pp. 56-71.Search in Google Scholar

[6] KOVALEVSKAYA, E.: Simultaneous Diophantine approximation in R2 × C × Qp, Tatra Mt. Math. Publ. 56 (2013), 79-86.Search in Google Scholar

[7] SPRINDŽUK, V. G.: Mahler’s Problem in the Metric Theory of Numbers. Sci. and Technics, Minsk, 1965 (In Russian); AMS Transl. of Math. Monographs, Vol. 25, Amer. Math. Soc., Providence, R. I., 1969.Search in Google Scholar

[8] ŽELUDEVICH, F.: Simultane diophantishe Approximationen abhängiger Grössen in mehreren Metriken, Acta Arithm. 46 (1986), 285-296.10.4064/aa-46-3-285-296Search in Google Scholar

[9] BERNIK, V. I.-DODSON, M. M.: Metric Diophantine Approximation of Manifolds, in: Cambridge Tracts in Math., Vol. 137, Cambridge University Press, Cambridge, 1999.10.1017/CBO9780511565991Search in Google Scholar

[10] MOHAMMADI, A.-SALEHI GOLSEFIDI, A.: Simultaneous diophantine approximation in non-degenerate p-adic manifolds. Israil J. Math.188 (2012), 231-258.10.1007/s11856-011-0150-1Search in Google Scholar