THE COEFFICIENTS OF THE ω(q) MOCK THETA FUNCTION

In 1920, Ramanujan wrote to Hardy about his discovery of the mock theta functions. In the years since, there has been much work in understanding the transformation properties and asymptotic nature of these functions. Recently, Zwegers proved a relationship between mock theta functions and vector-valued modular forms, and Bringmann and Ono used the theory of Maass forms and Poincare series to prove a conjecture of Andrews, yielding an exact formula for the coefficients of the f(q) mock theta function. Here we build upon these results, using the theory of vector-valued modular forms and Poincare series to prove an exact formula for the coefficients of the omega(q) mock theta function.