LOCAL ZETA-FUNCTIONS ON HERMITIAN-FORMS AND ITS APPLICATION TO LOCAL-DENSITIES

We give an explicit description of functional equations satisfied by z eta Functions on the space of unramified hermitian forms over a p-adic field. Further, as an application, we give explicit expressions of lo cal densities of integral representations of nondegenerate unramified hermitian matrices with entries in the ring of p-adic integers. (C) 19 98 Academic Press.