The $2$-fold Bailey lemma and mock theta functions

2020 ◽  
Vol 50 (4) ◽  
pp. 1491-1496
Author(s):  
Zhizheng Zhang ◽  
Hanfei Song
Keyword(s):  
Theta Functions ◽  
Mock Theta Functions ◽  
Bailey Lemma

scholarly journals Higher depth mock theta functions and q-hypergeometric series

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Joshua Males ◽  
Andreas Mono ◽  
Larry Rolen
Keyword(s):  
Theta Function ◽  
Modular Forms ◽  
Hypergeometric Series ◽  
Theta Functions ◽  
Mock Theta Function ◽  
Mock Theta Functions ◽  
Maass Forms ◽  
Mock Modular Forms ◽  
Harmonic Maass Forms

Abstract In the theory of harmonic Maaß forms and mock modular forms, mock theta functions are distinguished examples which arose from q-hypergeometric examples of Ramanujan. Recently, there has been a body of work on higher depth mock modular forms. Here, we introduce distinguished examples of these forms, which we call higher depth mock theta functions, and develop q-hypergeometric expressions for them. We provide three examples of mock theta functions of depth two, each arising by multiplying a classical mock theta function with a certain specialization of a universal mock theta function. In addition, we give their modular completions, and relate each to a q-hypergeometric series.

Tenth Order Mock Theta Functions: Part IV

2018 ◽  
pp. 229-248
Author(s):  
George E. Andrews ◽  
Bruce C. Berndt
Keyword(s):  
Theta Functions ◽  
Mock Theta Functions

scholarly journals CERTAIN RELATIONS FOR MOCK THETA FUNCTIONS OF ORDER EIGHT

2009 ◽  
Vol 24 (4) ◽  
pp. 629-640
Author(s):  
Maheshwar Pathak ◽  
Pankaj Srivastava
Keyword(s):  
Theta Functions ◽  
Mock Theta Functions

scholarly journals Congruences for sixth order mock theta functions $ \lambda(q) $ and $ \rho(q) $

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Harman Kaur ◽  
Meenakshi Rana
Keyword(s):  
Theta Functions ◽  
Sixth Order ◽  
Mock Theta Functions ◽  
Lost Notebook

<p style='text-indent:20px;'>Ramanujan introduced sixth order mock theta functions <inline-formula><tex-math id="M3">\begin{document}$ \lambda(q) $\end{document}</tex-math></inline-formula> and <inline-formula><tex-math id="M4">\begin{document}$ \rho(q) $\end{document}</tex-math></inline-formula> defined as:</p><p style='text-indent:20px;'><disp-formula> <label/> <tex-math id="FE1"> \begin{document}$ \begin{align*} \lambda(q) &amp; = \sum\limits_{n = 0}^{\infty}\frac{(-1)^n q^n (q;q^2)_n}{(-q;q)_n},\\ \rho(q) &amp; = \sum\limits_{n = 0}^{\infty}\frac{ q^{n(n+1)/2} (-q;q)_n}{(q;q^2)_{n+1}}, \end{align*} $\end{document} </tex-math></disp-formula></p><p style='text-indent:20px;'>listed in the Lost Notebook. In this paper, we present some Ramanujan-like congruences and also find their infinite families modulo 12 for the coefficients of mock theta functions mentioned above.</p>

scholarly journals Representations of affine superalgebras and mock theta functions II

2016 ◽  
Vol 300 ◽  
pp. 17-70 ◽  
Author(s):  
Victor G. Kac ◽  
Minoru Wakimoto
Keyword(s):  
Theta Functions ◽  
Mock Theta Functions

Asymptotic Transformations of q-Series

1998 ◽  
Vol 50 (2) ◽  
pp. 412-425 ◽  
Author(s):  
Richard J. McIntosh
Keyword(s):  
Asymptotic Expansion ◽  
Closed Form ◽  
Asymptotic Expansions ◽  
General Class ◽  
Theta Functions ◽  
Mock Theta Functions

AbstractFor the q–series we construct a companion q–series such that the asymptotic expansions of their logarithms as q → 1– differ only in the dominant few terms. The asymptotic expansion of their quotient then has a simple closed form; this gives rise to a new q–hypergeometric identity. We give an asymptotic expansion of a general class of q–series containing some of Ramanujan's mock theta functions and Selberg's identities.

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