Abstract: In 1984, Patterson and Piatetski-Shapiro constructed cuspidal distinguished representations on the three-fold covers of GL(3). Their construction is based on the work of Kazhdan and Patterson on metaplectic forms and the method of the converse theorems given by Jacquet, Piatetski-Shapiro, and Shalika. These distinguished representations can be viewed as generalizations of classical theta functions. This dissertation consists of two parts. In the first part, we apply the approach of Patterson and Piatetski-Shapiro to the case of the two fold cover of GL(2). We show that each Hecke character corresponds to a distinguished representation on the two-fold cover of GL(2). If the Hecke character is odd, then the corresponding distinguished representation is cuspidal. The same result has been obtained by Gelbart and Piatetski-Shapiro with a different approach using Weil representations. In the second part, we make progress toward generalizing the work of Patterson and Piatetski-Shapiro to the case of the four-fold cover of GL(4). The goal is to develop the relevant local Rankin-Selberg theory, adapt the converse theorem of Cogdell and Piatetski-Shapiro to the metaplectic setting and verify the analytic information needed to construct cuspidal distinguished representations by the converse theorem.