BYU

Abstract by Adam Skousen

Personal Infomation


Presenter's Name

Adam Skousen

Degree Level

Undergraduate

Abstract Infomation


Department

Mathematics

Faculty Advisor

Michael Griffin

Title

P-adic convergence of Hecke operators

Abstract

            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.