Generating functions and congruences for some partition functions related to mock theta functions

Effective Congruences for Mock Theta Functions

LetM(q) = ∑ c(n)q be one of Ramanujan’s mock theta functions. We establish the existence of infinitely many linear congruences of the form:

n-Color Partition Theoretic Interpretations of some Mock Theta Functions

Using n-color partitions we provide new number theoretic interpretations of four mock theta functions of S. Ramanujan.

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...