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Open Access Open Badges Research Article

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

Pentti Haukkanen

Author Affiliations

Department of Mathematics, Statistics and Philosophy, University of Tampere, Tampere 33014, Finland

Journal of Inequalities and Applications 2006, 2006:25020  doi:10.1155/JIA/2006/25020

The electronic version of this article is the complete one and can be found online at: http://www.journalofinequalitiesandapplications.com/content/2006/1/25020

Received:10 November 2004
Revisions received:12 January 2005
Accepted:9 February 2005
Published:6 February 2006

© 2006 Haukkanen

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.

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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