Taylor coefficients of false Jacobi forms and ranks of unimodal sequences

TL;DR

This paper investigates the asymptotic behavior of Taylor coefficients of false Jacobi forms, linking them to moments of ranks in unimodal sequences, and provides asymptotic series for these moments.

Contribution

It introduces a new framework for the modularity of false theta functions and applies it to derive asymptotic series for rank moments of unimodal sequences.

Findings

Asymptotic series for rank moments of two types of unimodal sequences

Application of a new modularity framework to false Jacobi forms

Generation of moments of the rank for unimodal sequences

Abstract

We apply the new framework for modularity of false theta functions developed by the second author and Nazaroglu to study the asymptotic behavior of Taylor coefficients of false Jacobi forms. The examples we study generate moments of the rank for unimodal sequences. For two types of unimodal sequences, we prove asymptotic series for the rank moments.