Book Review: A course in $p$-adic analysis

MINI-COURSE: p-MODULAR REPRESENTATIONS OF p-ADIC GROUPS

1.1. The case ` 6= p. In this case, we are in the setting of the classical Local Langlands Correspondence, which can be stated (roughly) as follows: Let n ≥ 1. We then have an injective map (1)  continuous representations of Gal(Qp/Qp) on n-dimensional Q`-vector spaces, up to isomorphism  ↪−→  irreducible, admissible representations of GLn(Qp) on Q`-vector spaces, up to isomor...

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...

p-adic Shearlets

The field $Q_{p}$ of $p$-adic numbers is defined as the completion of the field of the rational numbers $Q$ with respect to the  $p$-adic norm $|.|_{p}$. In this paper, we study the continuous and discrete $p-$adic shearlet systems on $L^{2}(Q_{p}^{2})$. We also suggest discrete $p-$adic shearlet frames. Several examples are provided.

The p - adic upper half plane Course and Project

This space was first introduced by Mumford, where it plays a key role in the generalization to higher genus of Tate’s theory of p-adic uniformization of elliptic curves with semistable reduction. Slightly later, Drinfeld and Cerednik showed that appropriate quotients of this space by discrete arithmetic subgroups of PGL2(K) coming from quaternion algebras yield Shimura curves. Since that time, ...

p-adic Analysis in Arithmetic Geometry