Explicit Overconvergence Rates Related to Eisenstein Series

In this thesis, we study explicit overconvergence rates related to Eisenstein series. We start by providing the necessary theoretical background on the theory of overconvergent modular forms. This includes the theory of Katz expansions, which is the main tool in the rest of the thesis to deduce overconvergence rates. Our main object will then be the family of modular functions E∗ κ/V (E∗ κ), which is derived from the (p-stabilized) Eisenstein series. These functions appear naturally when one moves between different weights of overconvergent modular forms and hence a good understanding of them is crucial to the entire theory. In particular, their overconvergence rates show up when studying the slopes (i.e. the valuations of eigenvalues of a p-adic Hecke-operator) which have been the object of a lot of research.