On Traces of Singular Moduli

Abstract

This article is an overview of Zagier's and Kim's work on traces of singular moduli. We give more detailed or new proofs to some of their results and also describe some algorithms to compute spaces of Jacobi forms and weight $3/2$ modular forms. Also, for $p$ a prime dividing the order of the Monster group, we give an explicit construction of the Hauptmodul $j_p$ of ${\Gamma }_0(p{)}^{\ast }$ using Rademacher series and Rademacher sums.

Expository Article, 37 pages