On effective irrationality measures for some values of certain hypergeometric functions 

Author:  Heimonen, Ari^{1} 
Organizations: 
^{1}University of Oulu, Faculty of Science, Department of Mathematical Sciences 
Format:  ebook 
Version:  published version 
Access:  open 
Online Access:  PDF Full Text (PDF, 1 MB) 
Persistent link:  http://urn.fi/urn:isbn:9514247191 
Language:  English 
Published: 
1997

Publish Date:  19970320 
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 
Description: 
AbstractThe 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 nonarchimedean 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. see all

Series: 
Acta Universitatis Ouluensis. A, Scientiae rerum naturalium 
ISSNE:  1796220X 
ISBN:  9514247191 
ISBN Print:  951424589X 
Issue:  290 
Subjects:  
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. 