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  • Research Article
  • 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:

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

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Authors’ Affiliations

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

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