• Corpus ID: 115174821

Mock Theta Functions

@article{Zwegers2008MockTF,
  title={Mock Theta Functions},
  author={Sander P. Zwegers},
  journal={arXiv: Number Theory},
  year={2008}
}
  • S. Zwegers
  • Published 30 July 2008
  • Mathematics
  • arXiv: Number Theory
The mock theta functions were invented by the Indian mathematician Srinivasa Ramanujan, who lived from 1887 until 1920. He discovered them shortly before his death. In this dissertation, I consider several of the examples that Ramanujan gave of mock theta functions, and relate them to real-analytic modular forms of weight 1/2. In Chapter 1, I consider a sum, which was also studied by Lerch. This Lerch sum transforms almost as a Jacobi form under substitutions in (upsilon, nu, tau ). I show… 
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The importance of the transformation laws of Gordon and McIntosh plays a central role in clarifying how several infinite families of mock theta functions sit within the infinite dimensional spaces of Maass forms are clarified.
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  • Mathematics
    Philosophical Transactions of the Royal Society A
  • 2019
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The author revisited Ramanujan's asymptotic claim, and established a connection between mock theta functions and quantum modular forms, which were not defined until 90 years later in 2010 by Zagier.
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AbstractMock modular forms, which give the theoretical framework for Ramanujan’s enigmatic mock theta functions, play many roles in mathematics. We study their role in the context of modular
Contemporary Mathematics Ramanujan ’ s radial limits
Ramanujan’s famous deathbed letter to G. H. Hardy concerns the asymptotic properties of modular forms and his so-called mock theta functions. For his mock theta function f(q), he asserts, as q
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References

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On the seventh order mock theta functions
In a recent paper [H], we proved the "Mock Theta Conjectures". These are identities, stated by Ramanujan in his "lost notebook" JR2, pp. 19-20], involving two of the 5th order mock 0-functions. In
Tenth order mock theta functions in Ramanujan’s lost notebook (IV)
Ramanujan's lost notebook contains many results on mock theta functions. In particular, the lost notebook contains eight identities for tenth order mock theta functions. Previously the author proved
Tenth order mock theta functions in Ramanujan's Lost Notebook
Ramanujan's lost notebook contains many results on mock theta functions. In particular, the lost notebook contains eight identities for tenth order mock theta functions. Previously the author proved
Tenth Order Mock Theta Functions in Ramanujan's Lost Notebook II
In S. Ramanujan's last letter to G. H. Hardy [B4], Ramanujan proclaimed, ``I discovered very interesting functions recently which I call `Mock' -functions.'' He then provided a long list of ``third
Some Eighth Order Mock Theta Functions
A method is developed for obtaining Ramanujan's mock theta functions from ordinary theta functions by performing certain operations on their q‐series expansions. The method is then used to construct
MOCK θ-FUNCTIONS AND REAL ANALYTIC MODULAR
In this paper we examine three examples of Ramanujan’s third order mock θ-functions and relate them to Rogers’ false θ-series and to a real-analytic modular form of weight 1/2.
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