Vol. 11, No. 1, 2022

Download this article
Download this article For screen
For printing
Recent Issues
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
Rational approximations to two irrational numbers

Nikita Shulga

Vol. 11 (2022), No. 1, 1–10
Abstract

For real ξ we consider the irrationality measure function ψξ(t) = min 1qt,qqξ. We prove that in the case α ± β there exist arbitrary large values of t with

| 1 ψα(t) 1 ψβ(t)| 5( 1 5 1 2 )t.

The constant on the right-hand side is optimal.

Keywords
irrationality measure function, diophantine approximation, continued fractions
Mathematical Subject Classification
Primary: 11J06, 11J70
Milestones
Received: 7 April 2021
Revised: 9 June 2021
Accepted: 25 June 2021
Published: 30 March 2022
Authors
Nikita Shulga
Moscow Center for Fundamental and Applied Mathematics
Moscow
Russia