Extension of a proof of the Ramanujan congruences for multipartitions

TL;DR

This paper extends a recent elegant proof of Ramanujan congruences for the partition function to multipartition functions and certain prime power moduli, broadening the scope of these classical results.

Contribution

It introduces a method to generalize existing proofs of Ramanujan congruences to multipartitions and prime power moduli using classical modular form theory.

Findings

Generalization of Ramanujan congruences to multipartition functions

Extension of proof to prime power moduli

Preservation of elegant proof structure without Hecke operators

Abstract

Recently Lachterman, Schayer, and Younger published an elegant proof of the Ramanujan congruences for the partition function $p(n)$. Their proof uses only the classical theory of modular forms as well as a beautiful result of Choie, Kohnen, and Ono, without need for Hecke operators. In this paper we give a method for generalizing Lachterman, Schayer, and Younger's proof to include Ramanujan congruences for multipartition functions $p_k(n)$, and Ramanujan congruences for $p(n)$ modulo certain prime powers.