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Optimal mock Jacobi theta functions
Advances in Mathematics, 2020 We classify the optimal mock Jacobi forms of weight one with rational coefficients. The space they span is thirty-four-dimensional, and admits a distinguished basis parameterized by genus zero groups of isometries of the hyperbolic plane. We show that their Fourier coefficients can be expressed explicitly in terms of singular moduli, and obtain ...
Cheng, M.C.N., Duncan, J.F.R.
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ON GENERALIZED EIGHTH ORDER MOCK THETA FUNCTIONS [PDF]
Ural Mathematical Journal, 2020 In this paper we have generalized eighth order mock theta functions, recently introduced by Gordon and MacIntosh involving four independent variables. The idea of generalizing was to have four extra parameters, which on specializing give known functions and thus these results hold for those known functions.
Rawat, Pramod Kumar, Rawat, P. K.
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, 2002 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.
Zwegers, Sander +2 more
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Higher depth mock theta functions and $q$-hypergeometric series [PDF]
, 2021 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.
Mono, Andreas +2 more
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Representations of mock theta functions [PDF]
Advances in Mathematics, 2020 Motivated by the works of Liu, we provide a unified approach to find Appell-Lerch series and Hecke-type series representations for mock theta functions. We establish a number of parameterized identities with two parameters $a$ and $b$. Specializing the choices of $(a,b)$, we not only give various known and new representations for the mock theta ...
Chen, Dandan, Wang, Liuquan
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Superconformal algebras and mock theta functions [PDF]
Journal of Physics A: Mathematical and Theoretical, 2009 It is known that characters of BPS representations of extended superconformal algebras do not have good modular properties due to extra singular vectors coming from the BPS condition. In order to improve their modular properties we apply the method of Zwegers which has recently been developed to analyze modular properties of mock theta functions.
Eguchi, Tohru, Hikami, Kazuhiro
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Bilateral series in terms of mixed mock modular forms
Journal of Inequalities and Applications, 2016 The number of strongly unimodal sequences of weight n is denoted by u ∗ ( n ) $u^{*}(n)$ . The generating functions for { u ∗ ( n ) } n = 1 ∞ $\{u^{*}(n)\}_{n=1}^{\infty}$ are U ∗ ( q ) = ∑ n = 1 ∞ u ∗ ( n ) q n $U^{*}(q)=\sum_{n=1}^{\infty}u^{*}(n)q^{n}$
Bin Chen, Haigang Zhou
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ON THE TENTH-ORDER MOCK THETA FUNCTIONS [PDF]
Journal of the Australian Mathematical Society, 2017 Using properties of Appell–Lerch functions, we give insightful proofs for six of Ramanujan’s identities for the tenth-order mock theta functions.
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Applications of an identity of Andrews
Arab Journal of Mathematical Sciences, 2014 In this paper, we give a bilateral form of an identity of Andrews, which is a generalization of the 1ψ1 summation formula of Ramanujan. Using Andrews’ identity, we deduce some new identities involving mock theta functions of second order and finally, we ...
D.D. Somashekara, K. Narasimha Murthy
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Families of multisums as mock theta functions
Advances in Applied Mathematics, 2016 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Nancy S. S. Gu, Jing Liu
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