Fungrim home page

Fungrim entry: bd7d8e

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

\tau \in \mathbb{H}
Definitions:
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:
Entry(ID("bd7d8e"),
    Formula(Equal(Sub(Pow(EisensteinE(4, tau), 3), Pow(EisensteinE(6, tau), 2)), Mul(Div(27, 4), Pow(Mul(Mul(JacobiTheta(2, 0, tau), JacobiTheta(3, 0, tau)), JacobiTheta(4, 0, tau)), 8)))),
    Variables(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.

2019-10-05 13:11:19.856591 UTC