Asymptotics of Bailey-type mock theta functions

TL;DR

This paper derives asymptotic estimates for Fourier coefficients of two mixed mock modular forms using advanced analytical techniques, revealing cancellation phenomena and employing higher order expansions for precise results.

Contribution

It provides the first detailed asymptotic analysis of Bailey-type mock theta functions, utilizing Wright's circle method and modified Tauberian theorems.

Findings

Asymptotic estimates for Fourier coefficients are obtained.

Cancellation effects are identified in the estimates.

Higher order asymptotics for Jacobi theta functions are used to refine results.

Abstract

We compute asymptotic estimates for the Fourier coefficients of two mixed mock modular forms, which come from Bailey pairs derived by Lovejoy and Osburn. To do so, we employ the circle method due to Wright and a modified Tauberian theorem. We encounter cancellation in our estimates for one of the mock theta functions due to the auxiliary function $\theta_{n,p}$ arising from the splitting of Hickerson and Mortenson. We deal with this by using higher order asymptotic expansions for the Jacobi theta functions.