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 enc...

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Bibliographic Details
Published in:Proceedings of the National Academy of Sciences - PNAS 2013-04, Vol.110 (15), p.5765-5768
Main Authors: Griffin, Michael, Ono, Ken, Rolen, Larry
Format: Article
Language:English
Subjects:
Coefficients
Combinatorics
Fourier coefficients
Fourier series expansion
Infinity
Integers
Mathematical analysis
Mathematical functions
Mathematical theorems
Mathematicians
Physical Sciences
Ramanujan, Srinivasa (1887-1920)
Series convergence
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Summary: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 this understanding, little attention has been given to Ramanujan’s original definition. Here, we prove that Ramanujan’s examples do indeed satisfy his original definition.
ISSN:0027-8424
1091-6490
DOI:10.1073/pnas.1300345110