Congruences for sixth order mock theta functions $ \lambda(q) $ and $ \rho(q) $

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:

On Two Fifth Order Mock Theta Functions

We consider the fifth order mock theta functions χ0 and χ1, defined by Ramanujan, and find identities for these functions, which relate them to indefinite theta functions. Similar identities have been found by Andrews for the other fifth order mock theta functions and the seventh order functions.

The Tenth Order Mock Theta Functions Revisited

In this paper we consider the first four of the eight identities between the tenth order mock theta functions, found in Ramanujan’s lost notebook. These were originally proved by Choi. Here we give an alternative proof.

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