Fungrim entry: 83566f

\mathop{\operatorname{zeros}\,}\limits_{\tau \in \mathcal{F}} E_{8}\!\left(\tau\right) = \left\{{e}^{2 \pi i / 3}\right\}

TeX:

\mathop{\operatorname{zeros}\,}\limits_{\tau \in \mathcal{F}} E_{8}\!\left(\tau\right) = \left\{{e}^{2 \pi i / 3}\right\}

Definitions:

Fungrim symbol	Notation	Short description
`Zeros`	$\mathop{\operatorname{zeros}\,}\limits_{x \in S} f(x)$	Zeros (roots) of function
`EisensteinE`	$E_{k}\!\left(\tau\right)$	Normalized Eisenstein series
`ModularGroupFundamentalDomain`	$\mathcal{F}$	Fundamental domain for action of the modular group
`Exp`	${e}^{z}$	Exponential function
`Pi`	$\pi$	The constant pi (3.14...)
`ConstI`	$i$	Imaginary unit

Source code for this entry:

Entry(ID("83566f"),
    Formula(Equal(Zeros(EisensteinE(8, tau), ForElement(tau, ModularGroupFundamentalDomain)), Set(Exp(Div(Mul(Mul(2, Pi), ConstI), 3))))))

Topics using this entry

Eisenstein series

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

2021-03-15 19:12:00.328586 UTC