Asymptotics of Bailey-type mock theta functions

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.