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Effective Congruences for Mock Theta Functions [PDF]
Mathematics, 2013 Let M(q) = ∑c(n) qn be one of Ramanujan’s mock theta functions. We establish the existence of infinitely many linear congruences of the form: c(An + B) ≡ 0 (mod lj) where A is a multiple of l and an auxiliary prime, p.
Heidi Goodson +3 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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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
Pramod Kumar Rawat
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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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A note on two of Ramanujan’s mock theta functions
The Ramanujan Journal, 2023 Abstract In the “Lost” Notebook Ramanujan defined two mock theta functions (which we denote by φR and ξR) and gave relations connecting them to some of the sixth-order mock theta functions. It turns out that these mock theta functions are related to each other by modular transformation.
Richard J. McIntosh
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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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A Study of Generalized Partial Mock Theta Functions
Electronic Journal of Mathematical Analysis and Applications. S. Ramanujan in his last letter to G.H. Hardy has introduced sev-enteen mock theta functions of di erenct 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 ...
Swayamprabha Tiwari +2 more
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On Ramanujan’s definition of mock theta function [PDF]
Proceedings of the National Academy of Sciences, 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.
Wakimoto, Minoru, Kac, Victor
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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 ...
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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