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Fungrim entry: 26faf3

zerosτFE10 ⁣(τ)={i,e2πi/3}\mathop{\operatorname{zeros}\,}\limits_{\tau \in \mathcal{F}} E_{10}\!\left(\tau\right) = \left\{i, {e}^{2 \pi i / 3}\right\}
\mathop{\operatorname{zeros}\,}\limits_{\tau \in \mathcal{F}} E_{10}\!\left(\tau\right) = \left\{i, {e}^{2 \pi i / 3}\right\}
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
ConstIii Imaginary unit
Expez{e}^{z} Exponential function
ConstPiπ\pi The constant pi (3.14...)
Source code for this entry:
    Formula(Equal(Zeros(EisensteinE(10, tau), Var(tau), Element(tau, ModularGroupFundamentalDomain)), Set(ConstI, Exp(Div(Mul(Mul(2, ConstPi), ConstI), 3))))))

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

2019-09-22 15:43:45.410764 UTC