Parity of coefficients of mock theta functions

On Recursions for Coefficients of Mock Theta Functions

We use a generalized Lambert series identity due to the first author to present qseries proofs of recent results of Imamoğlu, Raum and Richter concerning recursive formulas for the coefficients of two 3rd order mock theta functions. Additionally, we discuss an application of this identity to other mock theta functions.

Ramanujan's mock theta functions.

In his famous deathbed letter, Ramanujan introduced the notion of a mock theta function, and he offered some alleged examples. Recent work by Zwegers [Zwegers S (2001) Contemp Math 291:268-277 and Zwegers S (2002) PhD thesis (Univ of Utrecht, Utrecht, The Netherlands)] has elucidated the theory encompassing these examples. They are holomorphic parts of special harmonic weak Maass forms. Despite...

Mock Theta Functions, Ranks, and Maass Forms

Superconformal Algebras and Mock Theta Functions

It is known that characters of BPS representations of extended superconformal algebras do not have good modular properties due to extra singular vectors coming from the BPS condition. In order to improve their modular properties we apply the method of Zwegers which has recently been developed to analyze modular properties of mock theta functions. We consider the case of N = 4 superconformal alg...

Mock Theta Functions and Quantum Modular Forms

Ramanujan’s last letter to Hardy concerns the asymptotic properties of modular forms and his ‘mock theta functions’. For the mock theta function f (q), Ramanujan claims that as q approaches an even-order 2k root of unity, we have f (q)− (−1)(1− q)(1− q)(1− q) · · · (1− 2q+ 2q − · · ·)= O(1). We prove Ramanujan’s claim as a special case of a more general result. The implied constants in Ramanuja...