Results 201 to 210 of about 22,163 (226)

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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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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The Cubic Symplectic Theta Function

Journal of Mathematical Sciences, 2004
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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 symplectic theta-functions

Journal of Soviet Mathematics, 1989
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DIFFERENTIAL EQUATIONS FOR CUBIC THETA FUNCTIONS

International Journal of Number Theory, 2011
We show that the cubic theta functions satisfy two distinct coupled systems of nonlinear differential equations. The resulting relations are analogous to Ramanujan's differential equations for Eisenstein series on the full modular group. We deduce the cubic analogs presented here from trigonometric series identities arising in Ramanujan's original ...
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The Borweins’ Cubic Theta Functions and q-Elliptic Functions

2001
We give two identities; one, originally due to Weierstrass, is old and one appears to be new. We use these identities to give proofs of some relations between the functions a(q), b (q) and c (q) of Borwein, Borwein and Garvan [4].
Richard Lewis, Zhi-Guo Liu
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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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A Finite Group Related to the Cubic Theta Function

Journal of Mathematical Sciences, 2006
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. Bibliography: 17 titles.
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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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