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

Abstract

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