An upper bound for the ℓp norm of a GCD related matrix

Haukkanen, Pentti (2006)
 
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Haukkanen, Pentti
2006

Journal of Inequalities and Applications 2006
25020
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doi:10.1155/JIA/2006/25020
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We find an upper bound for the ℓp norm of the n × n matrix whose ij entry is (i,j)s/[i,j]r, where (i,j) and [i,j] are the greatest common divisor and the least common multiple of i and j and where r and s are real numbers. In fact, we show that if r>1/p and s
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