Results 41 to 50 of about 314 (66)

On ranks and cranks of partitions modulo 4 and 8

, 2019
Mortenson, E.
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Arithmetic properties for Appell–Lerch sums

The Ramanujan Journal, 2021
An Appell-Lerch sum is a series of the form \[ AL(x,q,z)=\frac{1}{(q,q/z,q;q)_\infty}\sum_{n=-\infty}^\infty \frac{(-1)^{+1}q^{n(n+1)/2}z^{n+1}}{1-xzq^n}, \] with certain restrictions on \(x\) and \(z\), and where \[ (a_1,a_2,\ldots,a_k;q)_\infty=(a_1;q)_\infty(a_2;q)_\infty\cdots(a_k;q)_\infty \quad \text{and}\quad (a;q)_\infty=\prod_{n=0}^\infty(1-aq^
Ding, W. H., Xia, Ernest X. W.
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Ranks, cranks for overpartitions and Appell–Lerch sums

The Ramanujan Journal, 2021
The purpose of this paper is to dissect the generating functions for the rank and certain cranks of overpartitions mod 4 and 8, and derive identities therefrom. Define the rank of an overpartition to be the largest part of the overpartition, minus its number of parts.
Bian, Min, Fang, Houqing, Huang, Xiao Qian, Yao, Olivia X. M.   +3 more
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Generalizations of Mock Theta Functions and Appell–Lerch Sums

Bulletin of the Iranian Mathematical Society, 2023
Mock theta functions have been a continuing source of inspiration and have motivated a tremendous amount of research over a century. Ramanujan named and studied such functions, which can be represented by Eulerian forms, Appell-Lerch sums, Hecke-type double sums, and Fourier coefficients of meromorphic Jacobi forms.
Su-Ping Cui, Nancy S. S. Gu, Dazhao Tang
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Proof of a conjectural congruence of Chan for Appell–Lerch sums

International Journal of Number Theory, 2020
In 2012, Chan posed six conjectures on congruences for Appell–Lerch sums and five of them were proved by mathematicians. In this paper, we confirm the remaining conjectural congruence of Chan by utilizing an identity due to Hickerson and Mortenson and the theory of modular forms.
Yan Fan, Liuquan Wang, Ernest X. W. Xia
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Generalizations of some conjectures of Chan on congruences for Appell–Lerch sums

Journal of Mathematical Analysis and Applications, 2018
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Qu, Y. K., Wang, Y. J., Yao, Olivia X. M.   +2 more
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Two Identities Involving a Mordell Integral and Appell–Lerch Sums

2018
On page 202 in his Lost Notebook, Ramanujan recorded without proofs two modular transformations involving a Mordell integral, q-hypergeometric series, and generalized Lambert series. These two formulas were first proved by Y.-S. Choi [110], and in this chapter we relate his proofs.
George E. Andrews, Bruce C. Berndt
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Appell–Lerch sums and $$\mathcal {N}=2$$ moduli

Letters in Mathematical Physics
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Classification by ordinal sums of conjunctive and disjunctive functions for explainable AI and interpretable machine learning solutions

Knowledge-Based Systems, 2021
Miroslav Hudec, Anna Saranti, Andreas Holzinger   +2 more
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Introducing SummerTime: A package for high-precision computation of sums appearing in DRA method

Computer Physics Communications, 2016
Roman N Lee, Kirill T Mingulov
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