ASYMPTOTIC BEHAVIOR OF EIGENVALUES OF RECIPROCAL POWER LCM MATRICES
Glasgow mathematical journal, Tome 50 (2008) no. 1, pp. 163-174
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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.
HONG, SHAOFANG; LEE, K. S. ENOCH. ASYMPTOTIC BEHAVIOR OF EIGENVALUES OF RECIPROCAL POWER LCM MATRICES. Glasgow mathematical journal, Tome 50 (2008) no. 1, pp. 163-174. doi: 10.1017/S0017089507003953
@article{10_1017_S0017089507003953,
author = {HONG, SHAOFANG and LEE, K. S. ENOCH},
title = {ASYMPTOTIC {BEHAVIOR} {OF} {EIGENVALUES} {OF} {RECIPROCAL} {POWER} {LCM} {MATRICES}},
journal = {Glasgow mathematical journal},
pages = {163--174},
year = {2008},
volume = {50},
number = {1},
doi = {10.1017/S0017089507003953},
url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089507003953/}
}
TY - JOUR AU - HONG, SHAOFANG AU - LEE, K. S. ENOCH TI - ASYMPTOTIC BEHAVIOR OF EIGENVALUES OF RECIPROCAL POWER LCM MATRICES JO - Glasgow mathematical journal PY - 2008 SP - 163 EP - 174 VL - 50 IS - 1 UR - http://geodesic.mathdoc.fr/articles/10.1017/S0017089507003953/ DO - 10.1017/S0017089507003953 ID - 10_1017_S0017089507003953 ER -
%0 Journal Article %A HONG, SHAOFANG %A LEE, K. S. ENOCH %T ASYMPTOTIC BEHAVIOR OF EIGENVALUES OF RECIPROCAL POWER LCM MATRICES %J Glasgow mathematical journal %D 2008 %P 163-174 %V 50 %N 1 %U http://geodesic.mathdoc.fr/articles/10.1017/S0017089507003953/ %R 10.1017/S0017089507003953 %F 10_1017_S0017089507003953
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