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ERDŐS’ METHOD FOR DETERMINING THE IRRATIONALITY OF PRODUCTS

Part of: Diophantine approximation, transcendental number theory

Published online by Cambridge University Press:  13 July 2011

JAROSLAV HANČL  and
ONDŘEJ KOLOUCH
JAROSLAV HANČL*
Affiliation:
Department of Mathematics and Institute for Research and Applications of Fuzzy Modeling, University of Ostrava, 30. dubna 22, 701 03 Ostrava 1, Czech Republic (email: hancl@osu.cz)
ONDŘEJ KOLOUCH
Affiliation:
Department of Mathematics and Institute for Research and Applications of Fuzzy Modeling, University of Ostrava, 30. dubna 22, 701 03 Ostrava 1, Czech Republic (email: ondrej.kolouch@osu.cz)
*
✉For correspondence; e-mail: hancl@osu.cz
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Abstract

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This paper deals with a sufficient condition for the infinite product of rational numbers to be an irrational number. The condition requires only some conditions for convergence and does not use other properties like divisibility. The proof is based on an idea of Erdős.

Keywords

irrationalityinfinite products

MSC classification

Secondary: 11J72: Irrationality; linear independence over a field
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 84 , Issue 3 , December 2011 , pp. 414 - 424
Copyright
Copyright © Australian Mathematical Publishing Association Inc. 2011

Footnotes

The first author was supported by the grants no. ME09017 and MSM 6198898701.

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