Eulerian series as modular forms revisited

TL;DR

This paper revisits the connection between Eulerian series and modular forms, providing a shorter proof of a key theorem using Appell--Lerch sums and exploring links to recent research by Kang.

Contribution

It introduces a streamlined proof of a main theorem on Eulerian series as modular forms via Appell--Lerch sums, building on prior harmonic weak Maass form methods.

Findings

Shortened proof of a main theorem on Eulerian series as modular forms.

Establishment of connections between Appell--Lerch sums and modular forms.

Discussion of links to recent work by Kang.

Abstract

Recently, Bringmann, Ono, and Rhoades employed harmonic weak Maass forms to prove results on Eulerian series as modular forms. By changing the setting to Appell--Lerch sums, we shorten the proof of one of their main theorems. In addition we discuss connections to recent work of Kang.