- Research Article
- Open Access
An upper bound for the
norm of a GCD-related matrix
- Pentti Haukkanen1Email author
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.
Keywords
- Positive Integer
- Real Number
- Zeta Function
- Great Common Divisor
- Riemann Zeta Function
Authors’ Affiliations
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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.
