A note on bounds for norms of the reciprocal LCM matrix

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Altinisik E., TUĞLU N., Haukkanen P.

MATHEMATICAL INEQUALITIES & APPLICATIONS, vol.7, no.4, pp.491-496, 2004 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 7 Issue: 4
  • Publication Date: 2004
  • Doi Number: 10.7153/mia-07-48
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.491-496
  • Gazi University Affiliated: Yes


Let S = {x(1), x(2),...., x(n)} be a set of distinct positive integers and [x(i), x(j)] denote the least common multiple of x(i) and x(j). The matrix [S-1] = (s(ij)), where s(ij) = 1/[x(i),x(j)] called the reciprocal least common multiple (reciprocal LCM) matrix on S. In this paper, we investigate some matrix norms of the reciprocal LCM matrix and one of its generalizations on S = {1, 2,..., n} in terms of the Riemann zeta function.