Quadratic forms and four partition functions modulo 3

TL;DR

This paper generalizes recent congruences modulo 3 for four partition functions by leveraging arithmetic properties of quadratic forms, expanding understanding of partition congruences.

Contribution

It introduces a new approach using quadratic forms to extend known partition congruences modulo 3, building on previous elementary series methods.

Findings

Established generalized congruences for four partition functions

Connected quadratic forms with partition congruences

Enhanced the theoretical framework for partition congruences modulo 3

Abstract

Recently, Andrews, Hirschhorn and Sellers have proven congruences modulo 3 for four types of partitions using elementary series manipulations. In this paper, we generalize their congruences using arithmetic properties of certain quadratic forms.