University of Oulu

On effective irrationality measures for some values of certain hypergeometric functions

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Author: Heimonen, Ari1
Organizations: 1University of Oulu, Faculty of Science, Department of Mathematical Sciences
Format: ebook
Version: published version
Access: open
Online Access: PDF Full Text (PDF, 1 MB)
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Language: English
Published: 1997
Publish Date: 1997-03-20
Thesis type: Doctoral Dissertation
Defence Note: Academic Dissertation to be presented with the assent of the Faculty of Science, University of Oulu, for public discussion in Kajaaninsali (Auditorium L 6), on May 10th, 1997, at 12 noon.
Reviewer: Professor Seppo Hyyrö
Professor Georges Rhin


The dissertation consists of three articles in which irrationality measures for some values of certain special cases of the Gauss hypergeometric function are considered in both archimedean and non-archimedean metrics.

The first presents a general result and a divisibility criterion for certain products of binomial coefficients upon which the sharpenings of the general result in special cases rely. The paper also provides an improvement concerning th e values of the logarithmic function. The second paper includes two other special cases, the first of which gives irrationality measures for some values of the arctan function, for example, and the second concerns values of the binomial function. All the results of the first two papers are effective, but no computation of the constants for explicit presentation is carried out. This task is fulfilled in the third article for logarithmic and binomial cases. The results of the latter case are applied to some Diophantine equations.

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Series: Acta Universitatis Ouluensis. A, Scientiae rerum naturalium
ISSN-E: 1796-220X
ISBN: 951-42-4719-1
ISBN Print: 951-42-4589-X
Issue: 290
Copyright information: © University of Oulu, 1997. This publication is copyrighted. You may download, display and print it for your own personal use. Commercial use is prohibited.