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Mock theta functions and Appell–Lerch sums [PDF]
Journal of Inequalities and Applications, 2018 Recently, Mortenson (Proc. Edinb. Math. Soc. 4:1–13, 2015) explored the bilateral series in terms of Appell–Lerch sums for the universal mock theta function g2(x,q) $g_{2}{(x,q)}$.
Bin Chen
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On Ramanujan's definition of mock theta function. [PDF]
Proc Natl Acad Sci U S A, 2013 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.
Rhoades RC.
europepmc +16 more sources
A Mock Theta Function of Second Order [PDF]
International Journal of Mathematics and Mathematical Sciences, 2009 We consider the second-order mock theta function 𝒟5 (𝑞), which Hikami came across in his work on mathematical physics and quantum invariant of three manifold.
Bhaskar Srivastava
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On the tenth-order mock Theta functions [PDF]
Journal of the Australian Mathematical Society, 2018 Using properties of Appell–Lerch functions, we give insightful proofs for six of Ramanujan’s identities for the tenth-order mock theta functions.
Mortenson, E.
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MOCK THETA FUNCTIONS AND QUANTUM MODULAR FORMS [PDF]
Forum of Mathematics, Pi, 2013 Ramanujan’s last letter to Hardy concerns the asymptotic properties of modular forms and his ‘mock theta functions’. For the mock theta function $f(q)$, Ramanujan claims that as $q$ approaches an even-order $2k$ root of unity, we have $$\begin{eqnarray ...
AMANDA FOLSOM +2 more
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q-hypergeometric double sums as mock theta functions [PDF]
Pacific Journal of Mathematics, 2012 Recently, Bringmann and Kane established two new Bailey pairs and used them to relate certain q-hypergeometric series to real quadratic fields. We show how these pairs give rise to new mock theta functions in the form of q-hypergeometric double sums ...
Andrews +5 more
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Recurrence relations connecting mock theta functions and restricted partition functions [PDF]
Notes on Number Theory and Discrete Mathematics, 2023 In this paper, we provide some recurrence relations connecting restricted partition functions and mock theta functions. Elementary manipulations are used including Jacobi triple product identity, Euler's pentagonal number theorem, and Ramanujan's theta ...
M. Rana, H. Kaur, K. Garg
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Ramanujan’s mock theta functions [PDF]
Proceedings of the National Academy of Sciences, 2013 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 ...
Griffin, Michael, Ono, Ken, Rolen, Larry
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Some Special Integer Partitions Generated by a Family of Functions
Trends in Computational and Applied Mathematics, 2023 In this work, inspired by Ramanujan’s fifth order Mock Theta function f1(q), we define a collection of functions and look at them as generating functions for partitions of some integer n containing at least m parts equal to each one of the numbers from
M. L. Matte
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A domain free of the zeros of the partial theta function
Математичні Студії, 2023 The partial theta function is the sum of the series \medskip\centerline{$\displaystyle\theta (q,x):=\sum\nolimits _{j=0}^{\infty}q^{j(j+1)/2}x^j$,} \medskip\noi where $q$ is a real or complex parameter ($|q|
V. Kostov
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