Results 11 to 20 of about 808 (120)

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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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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Representations of mock theta functions [PDF]

Advances in Mathematics, 2017
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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Some identities associated with theta functions and tenth order mock theta functions [PDF]

Mathematica Moravica
The main objective of this paper is to present some identities associated with theta functions and tenth order mock theta functions. Several closely-related identities such as (for example) q-product identities and Jacobi's triple-product identity are ...
Chaudhary M.P., Guiben Salem, Mazhouda Kamel   +2 more
doaj   +1 more source

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
doaj   +1 more source

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
doaj   +1 more source

Squashed toric manifolds and higher depth mock modular forms

Journal of High Energy Physics, 2019
Squashed toric sigma models are a class of sigma models whose target space is a toric manifold in which the torus fibration is squashed away from the fixed points so as to produce a neck-like region.
Rajesh Kumar Gupta, Sameer Murthy, Caner Nazaroglu   +2 more
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Asymptotics for Bailey-type mock theta functions [PDF]

The Ramanujan Journal, 2021
AbstractWe compute asymptotic estimates for the Fourier coefficients of two mock theta functions, which come from Bailey pairs derived by Lovejoy and Osburn. To do so, we employ the circle method due to Wright and a modified Tauberian theorem. We encounter cancelation in our estimates for one of the mock theta functions due to the auxiliary function $$\
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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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A CHARACTERIZATION OF MODIFIED MOCK THETA FUNCTIONS [PDF]

Transformation Groups, 2016
We give a characterization of modified (in the sense of Zwegers) mock theta functions, parallel to that of ordinary theta functions. Namely, modified mock theta functions are characterized by their analyticity properties, elliptic transformation properties, and by being annihilated by certain second order differential operators.
Kac, Victor, Wakimoto, Minoru
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