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ASYMPTOTIC BEHAVIOR OF EIGENVALUES OF RECIPROCAL POWER LCM MATRICES

Published online by Cambridge University Press:  01 January 2008

SHAOFANG HONG  and
K. S. ENOCH LEE
SHAOFANG HONG*
Affiliation:
Mathematical College, Sichuan University, Chengdu 610064, P.R. China e-mail: s-f.hong@tom.com; hongsf02@yahoo.com
K. S. ENOCH LEE
Affiliation:
Department of Mathematics, Auburn University Montgomery, Montgomery, AL 36124-4023, USA e-mail: elee4@mail.aum.edu
*
The corresponding author is S. Hong who was supported by Program for New Century Excellent Talents in University Grant # NCET-06-0785 and by SRF for ROCS, SEM.
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Abstract

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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.

Keywords

Primary 11C2011A0515A36
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 50 , Issue 1 , January 2008 , pp. 163 - 174
Copyright
Copyright © Glasgow Mathematical Journal Trust 2008

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