Title: Rademacher Sums, Hecke Operators, and Moonshine
Student: Paul Bruno
Advisor: John Duncan (Assistant Professor, Emory University)
Abstract: In this talk, we analyze the actions of Hecke operators on Rademacher sums. To investigate the problem, we consider the coefficients of the Fourier expansion of a Rademacher sum. We derive explicit formulae for these coefficients and prove a number of relationships between them. Using this analysis, we identify distinguished families of Hecke operators for a large class of discrete groups of isometries of the hyperbolic plane.