Results 81 to 90 of about 33,042 (127)

ON SOME NEW MOCK THETA FUNCTIONS

Journal of the Australian Mathematical Society, 2018
In 1991, Andrews and Hickerson established a new Bailey pair and combined it with the constant term method to prove some results related to sixth-order mock theta functions. In this paper, we study how this pair gives rise to new mock theta functions in terms of Appell–Lerch sums.
NANCY S. S. GU, LI-JUN HAO
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New mock theta functions and formulas for basic hypergeometric series

Proceedings of the Edinburgh Mathematical Society, 2023
In recent years, mock theta functions in the modern sense have received great attention to seek examples of q-hypergeometric series and find their alternative representations.
O. Yao
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Transcendental formulas for the coefficients of Ramanujan’s mock theta functions

Research in Number Theory
Ramanujan’s 1920 last letter to Hardy contains seventeen examples of mock theta functions which he organized into three “orders.” The most famous of these is the third-order function f(q) which has received the most attention of any individual mock theta
Nickolas Andersen, Gradin Anderson
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The ranks of (a,b)-Fibonacci sequences and congruences for certain partition functions and Ramanujan's mock theta functions

Forum mathematicum
In this paper, employing some identities due to Newman, we present a new method for discovering infinite families of congruences and strange congruences for c ⁢ ( n ) {c(n)} which is defined by ∑ n = 0 ∞ c ⁢ ( n ) ⁢ q n = ∏ k = 1 ∞ ( 1 - q k ) r ⁢ ( 1 ...
E. X. Xia
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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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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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Some identities on the second order mock theta functions

The Ramanujan journal
Recently, Nath and Das investigated congruence properties for the second order mock theta function B(q). In their paper, they asked for analytic proofs of three identities on the second order mock theta functions A(q), B(q) and μ2(q)\documentclass[12pt ...
X. Cai, Eric H. Liu, O. Yao
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Some Eighth Order Mock Theta Functions

Journal of the London Mathematical Society, 2000
Summary: A method is developed for obtaining Ramanujan's mock theta functions from ordinary theta functions by performing certain operations on their \(q\)-series expansions. The method is then used to construct several new mock theta functions, including the first ones of eighth order.
Gordon, Basil, McIntosh, Richard J.
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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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THE COEFFICIENTS OF THE ω(q) MOCK THETA FUNCTION

International Journal of Number Theory, 2008
In 1920, Ramanujan wrote to Hardy about his discovery of the mock theta functions. In the years since, there has been much work in understanding the transformation properties and asymptotic nature of these functions. Recently, Zwegers proved a relationship between mock theta functions and vector-valued modular forms, and Bringmann and Ono used the ...
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