Vol. 9, No. 4, 2020

Download this article
Download this article For screen
For printing
Recent Issues
Volume 13, Issue 2
Volume 13, Issue 1
Volume 12, Issue 4
Volume 12, Issue 3
Volume 12, Issue 2
Volume 12, Issue 1
Volume 11, Issue 4
Volume 11, Issue 3
Volume 11, Issue 2
Volume 11, Issue 1
Volume 10, Issue 4
Volume 10, Issue 3
Volume 10, Issue 2
Volume 10, Issue 1
Volume 9, Issue 4
Volume 9, Issue 3
Volume 9, Issue 2
Volume 9, Issue 1
Volume 8, Issue 4
Volume 8, Issue 3
Volume 8, Issue 2
Volume 8, Issue 1
Older Issues
Volume 7, Issue 4
Volume 7, Issue 3
Volume 7, Issue 2
Volume 7, Issue 1
Volume 6, Issue 4
Volume 6, Issue 2-3
Volume 6, Issue 1
Volume 5, Issue 4
Volume 5, Issue 3
Volume 5, Issue 1-2
Volume 4, Issue 4
Volume 4, Issue 3
Volume 4, Issue 2
Volume 4, Issue 1
Volume 3, Issue 3-4
Volume 3, Issue 2
Volume 3, Issue 1
Volume 2, Issue 4
Volume 2, Issue 3
Volume 2, Issue 2
Volume 2, Issue 1
Volume 1, Issue 4
Volume 1, Issue 3
Volume 1, Issue 2
Volume 1, Issue 1
The Journal
About the journal
Ethics and policies
Peer-review process
 
Submission guidelines
Submission form
Editorial board
founded and published with the
scientific support and advice of
mathematicians from the
Moscow Institute of
Physics and Technology
Subscriptions
 
ISSN (electronic): 2996-220X
ISSN (print): 2996-2196
Author Index
To Appear
 
Other MSP Journals
Effective simultaneous rational approximation to pairs of real quadratic numbers

Yann Bugeaud

Vol. 9 (2020), No. 4, 353–360
Abstract

Let ξ, ζ be quadratic real numbers in distinct quadratic fields. We establish the existence of effectively computable, positive real numbers τ and c such that, for every integer q with q > c, we have

max{qξ,qζ} > q1+τ,

where denotes the distance to the nearest integer.

To the memory of Naum Ilich Feldman (1918–1994)

Keywords
simultaneous approximation, Pell equation, linear form in logarithms
Mathematical Subject Classification 2010
Primary: 11J13
Secondary: 11D09, 11J86
Milestones
Received: 29 July 2019
Revised: 9 March 2020
Accepted: 23 March 2020
Published: 5 November 2020
Authors
Yann Bugeaud
Institut de Recherche Mathématique Avancée, UMR 7501
Université de Strasbourg et CNRS
Strasbourg
France