SIMULTANEOUS DIOPHANTINE APPROXIMATION IN R2 × C × Qp

Ella Kovalevskaya

doi:10.2478/tmmp-2013-0028

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SIMULTANEOUS DIOPHANTINE APPROXIMATION IN R2 × C × Qp

Tatra Mountains Mathematical Publications

Volume 56 (2013): Issue 1 (November 2013)

By: Ella Kovalevskaya

Open Access

|Feb 2014

Abstract

An analogue of the convergence part of Khintchine’s theorem (1924) for simultaneous approximation of integral polynomials at the points (x1, x2, z,w) ∈ R2 × C × Qp is proved. It is a solution of the more general problem than Sprindźuk's problem (1980) in the ring of adeles. We use a new form of the essential and nonessential domain methods in metric theory of Diophantine approximation

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