Euler-like recurrences for smallest parts functions

TL;DR

This paper derives Euler-like recurrence relations for smallest parts functions using advanced modular form techniques, providing new insights into their structure and properties.

Contribution

It introduces novel recurrences for smallest parts functions based on holomorphic projection of non-holomorphic modular forms.

Findings

Derived Euler-like recurrences for smallest parts functions

Connected smallest parts functions to modular form theory

Enhanced understanding of the structure of smallest parts functions

Abstract

We obtain recurrences for smallest parts functions which resemble Euler's recurrence for the ordinary partition function. The proofs involve the holomorphic projection of non-holomorphic modular forms of weight 2.