A Survey of Classical Mock Theta Functions

Kac-Wakimoto characters and universal mock theta functions

“…We show that this is indeed the case. The universal mock theta functions g 2 (ω; q) and g 3 (ω; q) of Gordon and McIntosh [5] are generalizations of the original mock theta functions of Ramanujan. The original mock theta functions are basic hypergeometric-type series appearing in Ramanujan's notebooks and his last letter to Hardy.…”

“…The original mock theta functions are basic hypergeometric-type series appearing in Ramanujan's notebooks and his last letter to Hardy. The functions g 2 (ω; q) and g 3 (ω; q) are aptly named "universal", as it is shown by Gordon and McIntosh [5] that all classical mock theta functions of Ramanujan and subsequent natural generalizations may be written in terms of either g 2 (ω; q) or g 3 (ω; q), depending on the parity of their "order", a number assigned to each mock theta function. Both classically and in their more modern generalizations, mock theta functions have been objects of extensive research in the areas of number theory, combinatorics, and mathematical physics.…”

“…Both classically and in their more modern generalizations, mock theta functions have been objects of extensive research in the areas of number theory, combinatorics, and mathematical physics. We refer the reader to [16] and [5] for a more detailed account. The universal mock theta functions are defined by…”

“…For a precise definition of μ(u, v; τ ) and more on the work and results of Kang and Zwegers, see §2 below. In addition to results of Bringmann and Ono [3] and Gordon and McIntosh [5], we will use the work of Kang [11] and Zwegers [20] in the course of the proof of our main theorem, Theorem 1.1 below.…”

On recursions for coefficients of mock theta functions

“…is a 2nd order mock theta function (see [14]). To see this, replace q and b by q 4 and q, respectively in (4.2) to obtain…”