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.

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

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/