Open Access

An upper bound for the norm of a GCD-related matrix

Journal of Inequalities and Applications20062006:25020

https://doi.org/10.1155/JIA/2006/25020

Received: 10 November 2004

Accepted: 9 February 2005

Published: 6 February 2006

Abstract

We find an upper bound for the norm of the matrix whose entry is , where and are the greatest common divisor and the least common multiple of and and where and are real numbers. In fact, we show that if and , then for all positive integers , where is the Riemann zeta function.

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Authors’ Affiliations

(1)
Department of Mathematics, Statistics and Philosophy, University of Tampere

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Copyright

© Haukkanen 2006

This article is published under license to BioMed Central Ltd. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.