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Fungrim entry: 4da2cd

E4 ⁣(τ)=η16 ⁣(τ)η8 ⁣(2τ)+256η16 ⁣(2τ)η8 ⁣(τ)E_{4}\!\left(\tau\right) = \frac{\eta^{16}\!\left(\tau\right)}{\eta^{8}\!\left(2 \tau\right)} + 256 \frac{\eta^{16}\!\left(2 \tau\right)}{\eta^{8}\!\left(\tau\right)}
Assumptions:τH\tau \in \mathbb{H}
References:
  • K. Ono (2004), Web of Modularity: Arithmetic of the Coefficients of Modular Forms and q-series, American Mathematical Society. Theorem 1.67.
TeX:
E_{4}\!\left(\tau\right) = \frac{\eta^{16}\!\left(\tau\right)}{\eta^{8}\!\left(2 \tau\right)} + 256 \frac{\eta^{16}\!\left(2 \tau\right)}{\eta^{8}\!\left(\tau\right)}

\tau \in \mathbb{H}
Definitions:
Fungrim symbol Notation Short description
EisensteinEEk ⁣(τ)E_{k}\!\left(\tau\right) Normalized Eisenstein series
Powab{a}^{b} Power
DedekindEtaη ⁣(τ)\eta\!\left(\tau\right) Dedekind eta function
HHH\mathbb{H} Upper complex half-plane
Source code for this entry:
Entry(ID("4da2cd"),
    Formula(Equal(EisensteinE(4, tau), Add(Div(Pow(DedekindEta(tau), 16), Pow(DedekindEta(Mul(2, tau)), 8)), Mul(256, Div(Pow(DedekindEta(Mul(2, tau)), 16), Pow(DedekindEta(tau), 8)))))),
    Variables(tau),
    Assumptions(Element(tau, HH)),
    References("K. Ono (2004), Web of Modularity: Arithmetic of the Coefficients of Modular Forms and q-series, American Mathematical Society. Theorem 1.67."))

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2019-09-20 18:07:53.062439 UTC