An Introduction to p-adic Teichmüller Theory

$p$-adic Dual Shearlet Frames

We introduced the continuous and discrete $p$-adic shearlet systems. We restrict ourselves to a brief description of the $p$-adic theory and shearlets in real case. Using the group $G_p$ consist of all $p$-adic numbers that all of its elements have a square root, we defined the continuous $p$-adic shearlet system associated with $L^2left(Q_p^{2}right)$. The discrete $p$-adic shearlet frames for...

An introduction to Skolem’s p-adic method for solving Diophantine equations

In this thesis, an introduction to Skolem’s p-adic method for solving Diophantine equations is given. The main theorems that are proven give explicit algorithms for computing bounds for the amount of integer solutions of special Diophantine equations of the kind f(x, y) = 1, where f ∈ Z[x, y] is an irreducible form of degree 3 or 4 such that the ring of integers of the associated number field h...

p-adic Modular Forms: An Introduction

Serre in the 1970s was the first to formalize such a question on the way to constructing p-adic L-functions, by way of developing the notion of a p-adic modular form to be the p-adic limit of some compatible family of q-expansions of classical modular forms. Katz came along fairly soon afterwards and generalized the theory to a much more geometric context, and showed that Serre’s p-adic forms e...

Introduction to Teichmüller Theory

2 Can p - adic integrals be computed ?

This article gives an introduction to arithmetic motivic integration in the context of p-adic integrals that arise in representation theory. A special case of the fundamental lemma is interpreted as an identity of Chow motives.