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

Journal of Inequalities and Applications volume 2006, Article number: 25020 (2006) Cite this article

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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Affiliations

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

    Pentti Haukkanen

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  1. Pentti Haukkanen
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Correspondence to Pentti Haukkanen.

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Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License ( https://creativecommons.org/licenses/by/2.0 ), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Haukkanen, P. An upper bound for the norm of a GCD-related matrix. J Inequal Appl 2006, 25020 (2006). https://doi.org/10.1155/JIA/2006/25020

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

Keywords

  • Positive Integer
  • Real Number
  • Zeta Function
  • Great Common Divisor
  • Riemann Zeta Function