UCLA

In the 1970s Don Zagier introduced a family of Hilbert modular forms for real quadratic fields and a related family of elliptic modular forms. These forms possess a number of remarkable properties, and have inspired a great deal of research over the ensuing decades. After reviewing the necessary background material and introducing Zagier's work, this dissertation presents candidates for a generalization of these forms to real cubic fields, and studies some of their properties.