Ramanujan's illness.

On Ramanujan's definition of mock theta function.

In his famous "deathbed" letter, Ramanujan "defined" the notion of a mock theta function and offered some examples of functions he believed satisfied his definition. Very recently, Griffin et al. established for the first time that Ramanujan's mock theta functions actually satisfy his own definition. On the other hand, Zwegers' 2002 doctoral thesis [Zwegers S (2002) Mock theta functions. PhD th...

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...

Ramanujan’s Earlier Notebooks and His Lost Notebook

Since the centenary of Ramanujan's birth, a large amount of Ramanujan's mathematics that had been ensconced in his earlier notebooks and in his lost notebook has been brought to light. In particular, in 1987, only one book had been written on Ramanujan's notebooks [2], but now several have appeared [2], [1]. We now have a larger portion of Ramanujan's mathematics to appreciate, evaluate, analyz...

Holomorphic projections and Ramanujan's mock theta functions.

We use spectral methods of automorphic forms to establish a holomorphic projection operator for tensor products of vector-valued harmonic weak Maass forms and vector-valued modular forms. We apply this operator to discover simple recursions for Fourier series coefficients of Ramanujan's mock theta functions.

RAMANUJAN'S FUNCTION r{n)—k CONGRUENCE PROPERTY

ON RAMANUJAN'S Q{FUNCTIONy

This study provides a detailed analysis of a function which Knuth discovered to play a central r^ ole in the analysis of hashing with linear probing. The function, named after Knuth Q(n), is related to several of Ramanujan's investigations. It surfaces in the analysis of a variety of algorithms and discrete probability problems including hashing, the birthday paradox, random mapping statistics,...