Vol. 9, No. 4, 2020

Download this article
Download this article For screen
For printing
Recent Issues
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
The Journal
About the Journal
Editorial Board
Submission Guidelines
Submission Form
Policies for Authors
Ethics Statement
founded and published with the
scientific support and advice of the
Moscow Institute of
Physics and Technology
ISSN (electronic): 2640-7361
ISSN (print): 2220-5438
Previously Published
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

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)

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