Vol. 11, No. 2, 2022

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
This article is available for purchase or by subscription. See below.
Improved constants for effective irrationality measures from hypergeometric functions

Paul M. Voutier

Vol. 11 (2022), No. 2, 161–180
Abstract

We simplify and improve the constant c that appears in effective irrationality measures,

 |(a /b)mn p /q| > c |q |(κ+1),

obtained from the hypergeometric method for ab near 1. The dependence of c on |a| in our result is best possible (as is the dependence on n in many cases). For some applications, the dependence of this constant on |a| becomes important. We also establish some new inequalities for hypergeometric functions that are useful in other diophantine settings.

PDF Access Denied

We have not been able to recognize your IP address 3.230.173.188 as that of a subscriber to this journal.
Online access to the content of recent issues is by subscription, or purchase of single articles.

Please contact your institution's librarian suggesting a subscription, for example by using our journal-recom­mendation form. Or, visit our subscription page for instructions on purchasing a subscription.

You may also contact us at contact@msp.org
or by using our contact form.

Or, you may purchase this single article for USD 40.00:

Keywords
diophantine approximation, effective irrationality measures, hypergeometric functions
Mathematical Subject Classification
Primary: 11J82, 11J68, 33C05
Supplementary material

Appendix: Values of C_n, D_n and supporting data

Milestones
Received: 31 October 2021
Revised: 18 May 2022
Accepted: 1 June 2022
Published: 13 August 2022
Authors
Paul M. Voutier
London
United Kingdom