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Fungrim entry: 4a200a

zerosτFE4 ⁣(τ)={e2πi/3}\mathop{\operatorname{zeros}\,}\limits_{\tau \in \mathcal{F}} E_{4}\!\left(\tau\right) = \left\{{e}^{2 \pi i / 3}\right\}
TeX:
\mathop{\operatorname{zeros}\,}\limits_{\tau \in \mathcal{F}} E_{4}\!\left(\tau\right) = \left\{{e}^{2 \pi i / 3}\right\}
Definitions:
Fungrim symbol Notation Short description
ZeroszerosP(x)f ⁣(x)\mathop{\operatorname{zeros}\,}\limits_{P\left(x\right)} f\!\left(x\right) Zeros (roots) of function
EisensteinEEk ⁣(τ)E_{k}\!\left(\tau\right) Normalized Eisenstein series
ModularGroupFundamentalDomainF\mathcal{F} Fundamental domain for action of the modular group
Expez{e}^{z} Exponential function
ConstPiπ\pi The constant pi (3.14...)
ConstIii Imaginary unit
Source code for this entry:
Entry(ID("4a200a"),
    Formula(Equal(Zeros(EisensteinE(4, tau), tau, Element(tau, ModularGroupFundamentalDomain)), Set(Exp(Div(Mul(Mul(2, ConstPi), ConstI), 3))))))

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2019-09-16 21:17:18.797188 UTC