# Modular Forms and $k$-colored Generalized Frobenius Partitions

## TL;DR

This paper explores the generating functions of k-colored generalized Frobenius partitions using modular form theory, revealing new properties and deepening understanding of their mathematical structure.

## Contribution

It introduces novel properties of the generating functions for k-colored Frobenius partitions through modular form analysis.

## Key findings

- Discovery of new properties of generating functions
- Application of modular form theory to partition functions
- Enhanced understanding of partition function structure

## Abstract

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