<abstract xmlns="http://www.w3.org/1999/xhtml">We prove the convergence part of a Khintchine-type theorem for simultaneous Diophantine approximation of zero by values of integral polynomials at the points (x, z, ω1, ω2) ∈ R × C × Qp1 × Qp2 , where p1 ≠ p2 are primes. It is a generalization of Sprindžuk’s problem (1980) in the ring of adeles. We continue our investigation (2013), where the problem was proved at the points in R2 × C × Qp1 . We use the most precise form of the essential and inessential domains method in metric theory of Diophantine approximation. </abstract>

We prove the convergence part of a Khintchine-type theorem for simultaneous Diophantine approximation of zero by values of integral polynomials at the points (x, z, ω1, ω2) ∈ R × C × Qp1 × Qp2 , where p1 ≠ p2 are primes. It is a generalization of Sprindžuk’s problem (1980) in the ring of adeles. We continue our investigation (2013), where the problem was proved at the points in R2 × C × Qp1 . We use the most precise form of the essential and inessential domains method in metric theory of Diophantine approximation.

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

Byelorussian State Agricultural Technic University Nezavisimosty 99 BY–220023-Minsk Belarus

Tatra Mountains Mathematical Publications

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

{"article-title":"The Convergence Part of a Knintchine-Type Theorem in the Ring of Adeles"}

We prove the convergence part of a Khintchine-type theorem for simultaneous Diophantine approximation of zero by values of integral polynomials at the points...

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

Published Online: Mar 11, 2015

Page range: 39 - 50

Received: Aug 07, 2014

DOI: https://doi.org/10.2478/tmmp-2014-0017

© 2015

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.