We study modular Galois representations mod pm. We show that there are three
progressively weaker notions of modularity for a Galois representation mod pm: We have …

We investigate certain finiteness questions that arise naturally when studying
approximations modulo prime powers of-adic Galois representations coming from modular …

Abstract Recently, Chen and Kiming studied the theta operator on modular forms modulo
prime powers pm, where p≥ 5 and m≥ 2. In this paper, we study mod pm filtrations and …

The notions of strong, weak and dc-weak eigenforms mod $ p^ n $ was introduced and
studied by Chen, Kiming and Wiese. In this work, we prove that there can be no uniform …

This thesis discusses the modular method and explores the different ways in which it can be
applied to solve Diophantine equations. In particular, the symplectic method will be …