Spherical functions and local densities on the space of p-adic quaternion Hermitian forms

Local Densities of 2-adic Quadratic Forms

In this paper, we give an explicit from formula for the local density number of representing a two by two 2-integral matrix T by a quadratic 2-integral lattice L over Z2. The non-dyadic case was dealt in a previous paper. The special case when L is a (maximal) lattice in the space of trace zero elements in a quaternion algebra over Q2 yields a clean and interesting formula, which matches up per...

Remarks on Macdonald’s book on p-adic spherical functions

When Ian Macdonald’s book Spherical functions on a group of p-adic type first appeared, it was one of a very small number of publications concerned with representations of p-adic groups. At just about that time, however, the subject began to bewidely recognized as indispensable in understanding automorphic forms, and the literature on the subject started to grow rapidly. Since it has by now gro...

GENERALIZED SPHERICAL FUNCTIONS ON REDUCTIVE p-ADIC GROUPS

Let G be the group of rational points of a connected reductive p-adic group and let K be a maximal compact subgroup satisfying conditions of Theorem 5 from Harish-Chandra (1970). Generalized spherical functions on G are eigenfunctions for the action of the Bernstein center, which satisfy a transformation property for the action of K. In this paper we show that spaces of generalized spherical fu...

SPHERICAL FUNCTIONS ON A p-ADIC CHEVALLEY GROUP

PSEUDO-DIFFERENTIAL EQUATIONS CONNECTED WITH p−ADIC FORMS AND LOCAL ZETA FUNCTIONS

We study the asymptotics of fundamental solutions of p-adic pseudodifferential equations of type (f(∂, β) + λ)u = g, where f(∂, β) is a pseudo-differential operator with symbol |f | K , β > 0, f is a form of arbitrary degree with coefficients in a p−adic field, λ ≥ 0, and g is a Schwartz-Bruhat function.