ASYMPTOTIC BEHAVIOR OF EIGENVALUES OF RECIPROCAL POWER LCM MATRICES

HONG, SHAOFANG ; LEE, K. S. ENOCH

Glasgow mathematical journal, Tome 50 (2008) no. 1, pp. 163-174

Résumé

Let be an arbitrary strictly increasing infinite sequence of positive integers. For an integer n≥1, let . Let r>0 be a real number and q≥ 1 a given integer. Let be the eigenvalues of the reciprocal power LCM matrix having the reciprocal power of the least common multiple of xi and xj as its i, j-entry. We show that the sequence converges and . We show that the sequence converges if and . We show also that if r> 1, then the sequence converges and , where t and l are given positive integers such that t≤l−1.

Détail

DOI : 10.1017/S0017089507003953

Mots-clés : Primary 11C20, 11A05, 15A36

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