Abstract by Adam Skousen
P-adic convergence of Hecke operators
A modular form is a complex valued function defined on the upper half plane that satisfies certain symmetries. The Fourier coefficients of many interesting modular forms are all integers. The Hecke operators are multiplicative operators that preserve spaces of modular forms. The action of a Hecke operator on a form can be described by its effect on the Fourier coefficients. In certain cases, the repeated application of the Hecke operators can cause the coefficients of a modular form to converge p-adically.