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

Abstract

summary: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.