Results 141 to 150 of about 44,715 (186)

Maass forms and the mock theta function f(q)

Mathematische Annalen, 2018
Let $$f(q):=1+\sum _{n=1}^{\infty } \alpha (n)q^n$$f(q):=1+∑n=1∞α(n)qn be the well-known third order mock theta of Ramanujan. In 1964, George Andrews proved an asymptotic formula of the form $$\begin{aligned} \alpha (n)= \sum _{c\le \sqrt{n}} \psi (n)+O_\
S. Ahlgren, Alexander Dunn
semanticscholar   +2 more sources

On congruences of sixth order mock theta function

Boletim da Sociedade Paranaense de Matemática
In a recent work, Kaur and Rana, obtained several Ramanujan-like congruences and established infinite families of congruences modulo 12 for the coefficients of sixth order mock theta functions λ(q) and ρ(q).
Yudhisthira Jamudulia, Gouri Shankar Guru   +1 more
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ARITHMETIC PROPERTIES OF COEFFICIENTS OF THE MOCK THETA FUNCTION $B(q)$

Bulletin of the Australian Mathematical Society, 2019
We investigate the arithmetic properties of the second-order mock theta function $B(q)$ and establish two identities for the coefficients of this function along arithmetic progressions. As applications, we prove several congruences for these coefficients.
Renrong Mao
semanticscholar   +1 more source

New Fifth and Seventh Order Mock Theta Function Identities

Annals of Combinatorics, 2019
We give simple proofs of Hecke–Rogers indefinite binary theta series identities for the two Ramanujan’s fifth order mock theta functions χ0(q)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage ...
F. Garvan
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MOCK MAASS THETA FUNCTIONS

The Quarterly Journal of Mathematics, 2011
The purpose of this paper is to use a general class of indefinite theta functions to explain and generalize an example of a Maass waveform that was constructed by Cohen from two functions σ and σ*, studied by Andrews, Dyson and Hickerson. For this, we construct certain functions attached to an indefinite binary quadratic form and show that they are ...
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Congruence properties of coefficients of the eighth-order mock theta function $$V_0(q)$$ V 0

The Ramanujan journal, 2019
We study the divisibility properties of the partition function associated with the eighth-order mock theta function $$V_0(q)$$ V 0 ( q ) , introduced by Gordon and McIntosh.
B. Hemanthkumar
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Mock Theta Functions and Mock Modular Forms

2012
In 1920, three months before his untimely death, Ramanujan hastily described the beginnings of a new theory he called “mock theta functions.” In 2001, Zwegers in his doctoral thesis, discovered the relation between non-holomorphic modular forms, indefinite theta series, and “mock theta functions.” We briefly describe this development in this chapter.
M. Ram Murty, V. Kumar Murty
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Mock Theta Function Identities Deriving from Bilateral Basic Hypergeometric Series

, 2016
The bilateral series corresponding to many of the third-, fifth-, sixth- and eighth order mock theta functions may be derived as special cases of $_2\psi_2$ series \[ \sum_{n=-\infty}^{\infty}\frac{(a,c;q)_n}{(b,d;q)_n}z^n.
J. Laughlin
semanticscholar   +1 more source

Fifth Order Mock Theta Functions: Proof of the Mock Theta Conjectures

2018
In Chapter 3, Section 3.1, we defined Ramanujan’s ten fifth order mock theta functions, and in Chapter 5 we stated the ten mock theta conjectures. The point of the latter chapter was to reveal that the conjectures could be separated into two groups of 5 each and that the conjectures within each group are equivalent.
George E. Andrews, Bruce C. Berndt
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Generalizations of mock theta functions

International Journal of Number Theory
Mock theta functions were first introduced by Ramanujan in his last paper to Hardy. Moreover, some other mock theta functions were presented in his lost notebook. It is well known that all the classical mock theta functions can be expressed by the universal mock theta functions [Formula: see text] and [Formula: see text].
Su-Ping Cui, Nancy S. S. Gu, Chen-Yang Su, Matthew H. Y. Xie   +3 more
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