Results 21 to 30 of about 33,042 (127)

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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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

New proofs for three identities of seventh order mock theta functions

AIMS Mathematics, 2023
Using the three-term Weierstrass relation for theta functions and the properties of Hecke-type double sums and Appell-Lerch sums, we give new and simple proofs for the seventh order mock theta conjectures.
Li-Jun Hao
semanticscholar   +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

CERTAIN RESULTS INVOLVING q-HYPERGEOMETRIC SERIES AND RAMANUJAN’S MOCK THETA FUNCTIONS

South East Asian J. of Mathematics and Mathematical Sciences, 2023
In this paper certain transformation formulas for q-hypergeometric series have been established. In another section of this paper, results involving mock theta functions have also been established.
Sunil Singh, Mohmmad Shahjade, Amit Kumar Singh   +2 more
semanticscholar   +1 more source

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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Bilateral Two-Parameter Mock Theta Functions and Related Applications [PDF]

Symmetry, Integrability and Geometry: Methods and Applications
In this paper, we investigate new relationships for bilateral series related to two-parameter mock theta functions, which lead to many identities concerning the bilateral mock theta functions. In addition, interesting relations between the classical mock
Chun Wang
semanticscholar   +1 more source

RELATIONSHIPS BETWEEN MOCK THETA FUNCTIONS AND q-CONTINUED FRACTIONS

JOURNAL OF RAMANUJAN SOCIETY OF MATHEMATICS AND MATHEMATICAL SCIENCES, 2023
The main object of this paper is to present five new interrelationships between mock theta functions and q-continued fractions.
S. Guiben
semanticscholar   +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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Congruences modulo powers of 5 and 7 for the crank and rank parity functions and related mock theta-functions [PDF]

The Ramanujan journal
It is well known that Ramanujan conjectured congruences modulo powers of 5, 7 and 11 for the partition function. These were subsequently proved by Watson (J. Reine Angew. Math. 179:97–128, 1938) and Atkin and O’Brien (Trans. Am. Math. Soc.
Dandan Chen, Rong Chen, F. Garvan
semanticscholar   +1 more source