Abstract
Redheffer introduced a sparse (0,1) matrix whose determinant provides an unorthodox representation of the Mertens function. The growth of the Mertens function is intimately tied to the locations of the nontrivial zeros of the Riemann zeta function.We introduce a (0,1) matrix whose determinant also provides a nontrivial representation of the Mertens function, but it is sparser than the matrix of Redheffer. It is sparser in two ways: the matrix has fewer nonzero entries (O(n) compared to O(nlogn)), and it has substantially fewer eigenvalues different from 1. This construction is a corollary of a more general result that holds for multiplicative sequences.
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