Fungrim home page

Fungrim entry: bd7d8e

E43 ⁣(τ)E62 ⁣(τ)=274(abc)8   where a=θ2 ⁣(0,τ),b=θ3 ⁣(0,τ),c=θ4 ⁣(0,τ)E_{4}^{3}\!\left(\tau\right) - E_{6}^{2}\!\left(\tau\right) = \frac{27}{4} {\left(a b c\right)}^{8}\; \text{ where } a = \theta_{2}\!\left(0 , \tau\right),\,b = \theta_{3}\!\left(0 , \tau\right),\,c = \theta_{4}\!\left(0 , \tau\right)
Assumptions:τH\tau \in \mathbb{H}
E_{4}^{3}\!\left(\tau\right) - E_{6}^{2}\!\left(\tau\right) = \frac{27}{4} {\left(a b c\right)}^{8}\; \text{ where } a = \theta_{2}\!\left(0 , \tau\right),\,b = \theta_{3}\!\left(0 , \tau\right),\,c = \theta_{4}\!\left(0 , \tau\right)

\tau \in \mathbb{H}
Fungrim symbol Notation Short description
Powab{a}^{b} Power
EisensteinEEk ⁣(τ)E_{k}\!\left(\tau\right) Normalized Eisenstein series
JacobiThetaθj ⁣(z,τ)\theta_{j}\!\left(z , \tau\right) Jacobi theta function
HHH\mathbb{H} Upper complex half-plane
Source code for this entry:
    Formula(Equal(Sub(Pow(EisensteinE(4, tau), 3), Pow(EisensteinE(6, tau), 2)), Where(Mul(Div(27, 4), Pow(Mul(Mul(a, b), c), 8)), Equal(a, JacobiTheta(2, 0, tau)), Equal(b, JacobiTheta(3, 0, tau)), Equal(c, JacobiTheta(4, 0, tau))))),
    Assumptions(Element(tau, HH)))

Topics using this entry

Copyright (C) Fredrik Johansson and contributors. Fungrim is provided under the MIT license. The source code is on GitHub.

2019-08-19 14:38:23.809000 UTC