We attach a certain n × n matrix An to the Dirichlet series L(s) = ∑ ∞ k=1 akk . We study the determinant, characteristic polynomial, eigenvalues, and eigenvectors of these matrices. The determinant of An can be understood as a weighted sum of the first n coefficients of the Dirichlet series L(s). We give an interpretation of the partial sum of a Dirichlet series as a product of eigenvalues. In...