Modular Forms and $k$-colored Generalized Frobenius Partitions

Abstract

Let $k$ and $n$ be positive integers. Let $c{\varphi }_k(n)$ denote the number of $k$-colored generalized Frobenius partitions of $n$ and $\mathrm{C}{\Phi }_k(q)$ be the generating function of $c{\varphi }_k(n)$. In this article, we study $\mathrm{C}{\Phi }_k(q)$ using the theory of modular forms and discover new surprising properties of $\mathrm{C}{\Phi }_k(q)$.

46 pages. We added a section of corrigendum on the last page, which corrects several typos in the published version

References in corpus (1)

• An Unexpected Congruence Modulo 5 for 4--Colored Generalized Frobenius Partitions