Traces of partition Eisenstein series and almost holomorphic modular forms

TL;DR

This paper investigates the structure and properties of traces of partition Eisenstein series and almost holomorphic modular forms, providing explicit space classifications, modular completions, and operator relations.

Contribution

It precisely characterizes the spaces of these traces, constructs their modular completions, and explores their interrelations through operators, advancing understanding of their modular properties.

Findings

Determined the exact spaces containing traces of partition Eisenstein series.

Constructed modular completions for these traces.

Established relations between these forms via specific operators.

Abstract

Recently, Amderberhan, Griffin, Ono, and Singh started the study of "traces of partition Eisenstein series" and used it to give explicit formulas for many interesting functions. In this note we determine the precise spaces in which they lie, find modular completions, and show how they are related via operators.