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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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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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Mock Theta Functions and Mock Modular Forms
2012In 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
2018In 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 TheoryMock 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 +3 more
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100 Years of mock theta functions
The Ramanujan JournalzbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Quantum q-series and mock theta functions
Research in the Mathematical ScienceszbMATH Open Web Interface contents unavailable due to conflicting licenses.
Folsom, Amanda, Metacarpa, David
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Recent Work on Mock Theta Functions
2018The work of Ramanujan has had a wide ranging impact in many branches of mathematics. Among many fields of research influenced by Ramanujan, few are as currently vibratingly active as the area of mock theta functions. In this chapter, we provide a brief and incomplete account of this activity.
George E. Andrews, Bruce C. Berndt
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Bilateral Mock theta functions of order ``eleven''
The definition of a mock theta function goes back to the work of Ramanujan. Since then several authors have discovered various types of mock theta functions of different order. In this article, the authors obtain eight bilateral mock theta functions of order ``eleven'' as the limiting cases of basic hypergeometric series \(_{6}\Phi_{5}\).Shukla, D. P., Ahmad, M.
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Partial theta functions and mock modular forms as q-hypergeometric series
Ramanujan Journal, 2012Amanda Folsom
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