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Mock Theta Functions and Mock Modular Forms

2012
In 1920, three months before his untimely death, Ramanujan hastily described the beginnings of a new theory he called “mock theta functions.” In 2001, Zwegers in his doctoral thesis, discovered the relation between non-holomorphic modular forms, indefinite theta series, and “mock theta functions.” We briefly describe this development in this chapter.
M. Ram Murty, V. Kumar Murty
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Fifth Order Mock Theta Functions: Proof of the Mock Theta Conjectures

2018
In Chapter 3, Section 3.1, we defined Ramanujan’s ten fifth order mock theta functions, and in Chapter 5 we stated the ten mock theta conjectures. The point of the latter chapter was to reveal that the conjectures could be separated into two groups of 5 each and that the conjectures within each group are equivalent.
George E. Andrews, Bruce C. Berndt
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Generalizations of mock theta functions

International Journal of Number Theory
Mock theta functions were first introduced by Ramanujan in his last paper to Hardy. Moreover, some other mock theta functions were presented in his lost notebook. It is well known that all the classical mock theta functions can be expressed by the universal mock theta functions [Formula: see text] and [Formula: see text].
Su-Ping Cui, Nancy S. S. Gu, Chen-Yang Su, Matthew H. Y. Xie   +3 more
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100 Years of mock theta functions

The Ramanujan Journal
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Some Eighth Order Mock Theta Functions

Journal of the London Mathematical Society, 2000
Summary: 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 several new mock theta functions, including the first ones of eighth order.
Gordon, Basil, McIntosh, Richard J.
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MOCK MAASS THETA FUNCTIONS

The Quarterly Journal of Mathematics, 2011
The purpose of this paper is to use a general class of indefinite theta functions to explain and generalize an example of a Maass waveform that was constructed by Cohen from two functions σ and σ*, studied by Andrews, Dyson and Hickerson. For this, we construct certain functions attached to an indefinite binary quadratic form and show that they are ...
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Quantum q-series and mock theta functions

Research in the Mathematical Sciences
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Folsom, Amanda, Metacarpa, David
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THE COEFFICIENTS OF THE ω(q) MOCK THETA FUNCTION

International Journal of Number Theory, 2008
In 1920, Ramanujan wrote to Hardy about his discovery of the mock theta functions. In the years since, there has been much work in understanding the transformation properties and asymptotic nature of these functions. Recently, Zwegers proved a relationship between mock theta functions and vector-valued modular forms, and Bringmann and Ono used the ...
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A Study of Generalized Partial Mock Theta Functions

Electronic Journal of Mathematical Analysis and Applications
Summary: S. Ramanujan in his last letter to G. H. Hardy has introduced seventeen mock theta functions of different orders (3, 5 and 7) without explicitly mentioning the reason for his levelling of order, later Watson added to this set three more third order mock theta function. \textit{G. N. Watson} [J. Lond. Math. Soc. 11, 55--80 (1936; Zbl 0013.11502)
Ahmad, Mohammad, Saba, Sameena, Tiwari, Swayamprabha   +2 more
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Mock theta functions -- an analytical point of view

1994
Summary: An analytical point of view on mock theta functions has been presented.
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