The Igusa Local Zeta Function Associated with the Singular Cases of the Determinant and the Pfaffian Original Research Article

This paper describes the theory of the Igusa local zeta function associated with a polynomialf(x) with coefficients in ap-adic local fieldK. Results are given in two cases wheref(x) is the determinant of a Hermitian matrix of degreemwith coefficients in: (1) a ramified quadratic extension ofK; and (2) the unique quaternion division algebra overK.