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Theta vectors and quantum theta functions [PDF]

Journal of Physics A: Mathematical and General, 2005
LaTeX 21 pages, give more explicit explanations for notions given in the ...
Lee, Chang-Yeong, Kim, Hoil
openaire   +3 more sources

Ramanujan's mock theta functions. [PDF]

Proc Natl Acad Sci U S A, 2013
In his famous deathbed letter, Ramanujan introduced the notion of a mock theta function , and he offered some alleged examples. Recent work by Zwegers [Zwegers S (2001) Contemp Math 291:268–277 and Zwegers S (2002) PhD thesis (Univ of Utrecht, Utrecht, The Netherlands)] has elucidated the ...
Griffin M, Ono K, Rolen L.
europepmc   +4 more sources

Mock theta functions and Appell–Lerch sums [PDF]

Journal of Inequalities and Applications, 2018
Recently, Mortenson (Proc. Edinb. Math. Soc. 4:1–13, 2015) explored the bilateral series in terms of Appell–Lerch sums for the universal mock theta function g2(x,q) $g_{2}{(x,q)}$.
Bin Chen
doaj   +2 more sources

Recurrence relations connecting mock theta functions and restricted partition functions [PDF]

Notes on Number Theory and Discrete Mathematics, 2023
In this paper, we provide some recurrence relations connecting restricted partition functions and mock theta functions. Elementary manipulations are used including Jacobi triple product identity, Euler's pentagonal number theorem, and Ramanujan's theta ...
M. Rana, H. Kaur, K. Garg
doaj   +1 more source

Weakly θ-I-Closed Sets and Weakly θ-I-continuous functions with respect to an Ideal Topological Spaces

Ratio Mathematica, 2023
In this paper, we introduce \breve{\theta}-\mathcal{I}-closed sets, \breve{\theta}-\mathcal{I}-closed sets, \breve{\theta}-\mathcal{I}-continuous functions and \breve{\theta}-\mathcal{I}-continuous functions and investigate their properties and its ...
M Vijayasankari, G Ramkumar
doaj   +1 more source

A Neural Model of Intrinsic and Extrinsic Hippocampal Theta Rhythms: Anatomy, Neurophysiology, and Function

Frontiers in Systems Neuroscience, 2021
This article describes a neural model of the anatomy, neurophysiology, and functions of intrinsic and extrinsic theta rhythms in the brains of multiple species.
Stephen Grossberg
doaj   +1 more source

Modular forms of half-integral weight on Γ0(4) with few nonvanishing coefficients modulo ℓ

Open Mathematics, 2022
Let kk be a nonnegative integer. Let KK be a number field and OK{{\mathcal{O}}}_{K} be the ring of integers of KK. Let ℓ≥5\ell \ge 5 be a prime and vv be a prime ideal of OK{{\mathcal{O}}}_{K} over ℓ\ell . Let ff be a modular form of weight k+12k+\frac{1}
Choi Dohoon, Lee Youngmin
doaj   +1 more source

Elliptic Solutions of Dynamical Lucas Sequences

Entropy, 2021
We study two types of dynamical extensions of Lucas sequences and give elliptic solutions for them. The first type concerns a level-dependent (or discrete time-dependent) version involving commuting variables. We show that a nice solution for this system
Michael J. Schlosser, Meesue Yoo
doaj   +1 more source

EESTIMATES OF BEST APPROXIMATIONS OF FUNCTIONS WITH LOGARITHMIC SMOOTHNESS IN THE LORENTZ SPACE WITH ANISOTROPIC NORM

Ural Mathematical Journal, 2020
In this paper, we consider the anisotropic Lorentz space \(L_{\bar{p}, \bar\theta}^{*}(\mathbb{I}^{m})\) of periodic functions of \(m\) variables. The Besov space \(B_{\bar{p}, \bar\theta}^{(0, \alpha, \tau)}\) of functions with logarithmic smoothness is
Gabdolla Akishev
doaj   +1 more source

Approximation characteristics of the isotropic Nikol'skii-Besov functional classes

Karpatsʹkì Matematičnì Publìkacìï, 2021
In the paper, we investigates the isotropic Nikol'skii-Besov classes $B^r_{p,\theta}(\mathbb{R}^d)$ of non-periodic functions of several variables, which for $d = 1$ are identical to the classes of functions with a dominant mixed smoothness $S^{r}_{p ...
S.Ya. Yanchenko, O.Ya. Radchenko
doaj   +1 more source