A note on bounds for norms of the reciprocal LCM matrix

Abstract

Let S = {x1, x2, . . . , xn} be a set of distinct positive integers and [xi, xj] denote the least common multiple of xi and xj . The matrix [S−1] = (sij) , where sij = 1 [xi,xj] , is called the reciprocal least common multiple (reciprocal LCM) matrix on S. In this paper, we investigate some matrix norms of the reciprocal LCM matrix and one of its generalizations on S = {1, 2, . . . , n} in terms of the Riemann zeta function. Mathematics subject classification (2000): 11C20, 15A36, 15A60, 11A25.