A note on bounds for norms of the reciprocal LCM matrix

Abstract

Abstract. Let S = {x 1 , x 2 , . . . , x n } be a set of distinct positive integers and [x i , x j ] denote the least common multiple of x i and x j . The matrix, 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. (2000): 11C20, 15A36, 15A60, 11A25. Mathematics subject classification

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