Matrices and Convolutions of Arithmetic Functions
نویسنده
چکیده
The purpose of this paper is to relate certain matrices with integer entries to convolutions of arithmetic functions. Let n be a positive integer, let a, 3, and y be arithmetic functions (complex-valued functions with domain the set of positive integers), and let ari denote the 1 x n matrix [a(l) a(2) ... a(n)]. We define the n x n divisor matrix Dn = (d^) by di 1 if i\j, di otherwise. Both Dn and its inverse, Dn , are upper triangular matrices. The arithmetic functions Vk, a, and e are defined by Vk(n) = n for k = 0, 1, 2,
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