Research Article
Open Access
An upper bound for the
norm of a GCD-related matrix
- Pentti Haukkanen1Email author
Journal of Inequalities and Applications20062006:25020
https://doi.org/10.1155/JIA/2006/25020
© Haukkanen 2006
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.
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.
