Results 1 to 10 of about 10,838,318 (324)

On Some Expansion Formulas for Products of Jacobi’s Theta Functions [PDF]

Mathematics, 2023
In this paper, we establish several expansion formulas for products of the Jacobi theta functions. As applications, we derive some expressions of the powers of (q;q)∞ by using these expansion formulas.
Hong-Cun Zhai, Jian Cao, Sama Arjika
doaj   +2 more sources

A Family of Theta-Function Identities Based upon Combinatorial Partition Identities Related to Jacobi’s Triple-Product Identity

Mathematics, 2020
The authors establish a set of six new theta-function identities involving multivariable R-functions which are based upon a number of q-product identities and Jacobi’s celebrated triple-product identity.
Hari Mohan Srivastava, Rekha Srivastava, Mahendra Pal Chaudhary, Salah Uddin   +3 more
doaj   +2 more sources

On Ramanujan's definition of mock theta function. [PDF]

Proc Natl Acad Sci U S A, 2013
Rhoades RC.
europepmc   +2 more sources

A domain free of the zeros of the partial theta function

Математичні Студії, 2023
The partial theta function is the sum of the series \medskip\centerline{$\displaystyle\theta (q,x):=\sum\nolimits _{j=0}^{\infty}q^{j(j+1)/2}x^j$,} \medskip\noi where $q$ is a real or complex parameter ($|q|
V. Kostov
doaj   +1 more source

Automatic Proof of Theta-Function Identities [PDF]

Texts & Monographs in Symbolic Computation, 2018
This is a tutorial for using two new MAPLE packages, thetaids and ramarobinsids. The thetaids package is designed for proving generalized eta-product identities using the valence formula for modular functions. We show how this package can be used to find
Jie Frye, F. Garvan
semanticscholar   +1 more source

Inverse Numerical Range and Determinantal Quartic Curves

Mathematics, 2020
A hyperbolic ternary form, according to the Helton–Vinnikov theorem, admits a determinantal representation of a linear symmetric matrix pencil. A kernel vector function of the linear symmetric matrix pencil is a solution to the inverse numerical range ...
Mao-Ting Chien, Hiroshi Nakazato
doaj   +1 more source

Massive theta lifts

Journal of High Energy Physics, 2023
We use Poincaré series for massive Maass-Jacobi forms to define a “massive theta lift”, and apply it to the examples of the constant function and the modular invariant j-function, with the Siegel-Narain theta function as integration kernel.
Marcus Berg, Daniel Persson
doaj   +1 more source

A domain containing all zeros of the partial theta function [PDF]

Publicationes mathematicae (Debrecen), 2017
We consider the partial theta function, i.e. the sum of the bivariate series $\theta (q,z):=\sum_{j=0}^{\infty}q^{j(j+1)/2}z^j$ for $q\in (0,1)$, $z\in \mathbb{C}$.
V. Kostov
semanticscholar   +1 more source

The explicit form of the switching surface in admissible synthesis problem

Visnik Harkivsʹkogo Nacionalʹnogo Universitetu im. V.N. Karazina. Cepiâ Matematika, Prikladna Matematika i Mehanika, 2022
In this article we consider the problem related to positional synthesis and controllability function method and more precisely to admissible maximum principle.
V. I. Korobov, O. S. Vozniak
doaj   +1 more source

Some results concerning localization property of generalized Herz, Herz-type Besov spaces and Herz-type Triebel-Lizorkin spaces

Karpatsʹkì Matematičnì Publìkacìï, 2021
In this paper, based on generalized Herz-type function spaces $\dot{K}_{q}^{p}(\theta)$ were introduced by Y. Komori and K. Matsuoka in 2009, we define Herz-type Besov spaces $\dot{K}_{q}^{p}B_{\beta }^{s}(\theta)$ and Herz-type Triebel-Lizorkin spaces $\
A. Djeriou, R. Heraiz
doaj   +1 more source