Geodesic
Simultaneous inhomogeneous Diophantine approximation of the values of integral polynomials with respect to Archimedean and non-Archimedean valuations
Communications in Mathematics, Tome 14 (2006) no. 1, pp. 37-42

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We prove an analogue of the convergence part of Khintchine’s theorem for the simultaneous inhomogeneous Diophantine approximation on the Veronese curve $(x,x^2,\ldots ,x^n)$ with respect to the different valuations. It is an extension of the author’s earlier results.
Classification : 11J61, 11J83, 11K60
Keywords: inhomogeneous Diophantine approximation; Khintchine type theorem; metric theory of Diophantine approximation; p-adic numbers 
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     title = {Simultaneous inhomogeneous {Diophantine} approximation of the values of integral polynomials with respect to {Archimedean} and {non-Archimedean} valuations},
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Kovalevskaya, Ella; Bernik, Vasily. Simultaneous inhomogeneous Diophantine approximation of the values of integral polynomials with respect to Archimedean and non-Archimedean valuations. Communications in Mathematics, Tome 14 (2006) no. 1, pp. 37-42. http://geodesic.mathdoc.fr/item/COMIM_2006__14_1_a5/