Determinants of multiplicative Toeplitz matrices

Abstract

In this paper we study matrices A = (aij) whose (i, j) th-entry is a function of i/j; that is, aij = f(i/j) for some f: Q + → C. We obtain a formula for the truncated determinants in the case where f is multiplicative, linking them to determinants of truncated Toeplitz matrices. We apply our formula to obtain several determinants of number-theoretic matrices.