Squared Möbius Function for Half-Integral Matrices and Its Applications Original Research Article

We define an analogue of the square of the usual Möbius function on the set of non-degenerate half-integral matrices. By using this function, we give a reasonable expression of the Koecher–Maaß Dirichlet series for a Siegel Modular form. In addition, we give another proof to a main result of (T. Ibukiyama and H. Saito, 1995, Amer. J. Math.117, 1097–1155) on the zeta functions for symmetric matrices.