Results 211 to 220 of about 2,404,536 (228)

Cubic Identities of Theta Functions

The Ramanujan Journal, 1998
A number of useful and interesting cubic identities involving theta functions are available in Ramanujan's Lost Note book. In this paper several theorems are established, in order to prove, some of these cubic identities. For proving the theorems the author employed addition formulas, the Jacobi triple product identity and the quintuple product ...
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Cubic Analogues of the Jacobian Theta Function θ(z, q)

Canadian Journal of Mathematics, 1993
AbstractThere are three modular forms a(q), b(q), c(q) involved in the parametrization of the hypergeometric function analogous to the classical θ2(q), θ3(q), θ4(q) and the hypergeometric function We give elliptic function generalizations of a(q), b(q), c(q) analogous to the classical theta-function θ(z, q). A number of identities are proved.
Hirschhorn, Michael, Garvan, Frank, Borwein, Jon   +2 more
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On the zeros of the L-function associated with the cubic theta function

Journal of Mathematical Sciences, 2008
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Some new Eisenstein series containing the Borweins’ cubic theta functions and convolution sum $$\displaystyle {\sum _{i+4j=n}^{}\sigma (i)\sigma (j)}$$

Afrika Matematika, 2020
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Shruthi, Kumar, B. R. Srivatsa
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The Borweins' Cubic Theta Function Identity and Some Cubic Modular Identities of Ramanujan

The Ramanujan Journal, 2000
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On the Dirichlet series related to the cubic theta function

Journal of Mathematical Sciences, 2007
The paper studies the function L(τ;·) defined by the Dirichlet series $$L(\tau ;s) = \sum\limits_\nu {\frac{{\tau (\nu )}}{{\left\| \nu \right\|^s }}, s \in \mathbb{C}} $$ , where τ(υ) is the υth Fourier coefficient of the Kubota-Patterson cubic theta function. For this function, an exact and an approximate functional equations are derived.
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Computation of the zeros of the L-function associated with the cubic theta function

Journal of Mathematical Sciences, 2009
The paper considers the L-function associated with the Kubota-Patterson cubic theta function. A method for computing values of the L-function is developed, and some conjectures on the distribution of its zeros are advanced and supported by numerical results. Bibliography: 12 titles.
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The Cubic Theta-Function Analogues of Borwein, Borwein and Garvan

2017
Borwein, Borwein, and Garvan introduced three functions whose behaviour is somewhat analogous to the classical theta-functions. The three functions have proved to play a fairly important role in aspects of partition theory and related areas. They are studied for their properties and the many relations between them, and their implications in earlier and
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Cubic power series, euler product and ramanujan's theta-functions

2021
В статье рассматривается элементарный метод, базирующийся на свойствах кубических тэта-функций, в связи с получением новых формул, в которых через эйлерово произведение выражаются степенные ряды с коэффициентами, равными значениям функции суммы нечетных степеней делителей (или с коэффициентами, равными значениям теоретико-числовой тау-функции) на ...
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On a certain finite group connected with the cubic theta function.

2004
Summary: With the Kubota-Patterson cubic theta function 27 shifted theta functions are associated. Then a certain group of permutations of the shifted theta functions is defined in a natural way, which proves to be isometric to a subgroup of the known group of permutations of 27 lines on a cubic surface.
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