Ramanujan tau function

Giving the Fourier coefficients of the Ramanujan modular form

In mathematics, the Ramanujan tau function, studied by Srinivasa Ramanujan, is the function τ : N → Z {\displaystyle \tau :\mathbb {N} \to \mathbb {Z} } defined by ∑ n = 1 ∞ τ ( n ) q n = q ∏ n = 1 ∞ ( 1 − q n ) 24 = q ϕ ( q ) 24 = η ( z ) 24 = Δ ( z ) , {\displaystyle \sum _{n=1}^{\infty }\tau (n)q^{n}=q\prod _{n=1}^{\infty }(1-q^{n})^{24}=q\phi (q)^{24}=\eta (z)^{24}=\Delta (z),} where ϕ {\displaystyle \phi } is the Euler function, η {\displaystyle \eta } is the Dedekind eta function, Δ ( z ) {\displaystyle \Delta (z)} is the modular discrimi...

From Wikipedia

In mathematics, the Ramanujan tau function, studied by Srinivasa Ramanujan, is the function τ : N → Z {\displaystyle \tau :\mathbb {N} \to \mathbb {Z} } defined by ∑ n = 1 ∞ τ ( n ) q n = q ∏ n = 1 ∞ ( 1 − q n ) 24 = q ϕ ( q ) 24 = η ( z ) 24 = Δ ( z ) , {\displaystyle \sum _{n=1}^{\infty }\tau (n)q^{n}=q\prod _{n=1}^{\infty }(1-q^{n})^{24}=q\phi (q)^{24}=\eta (z)^{24}=\Delta (z),} where ϕ {\displaystyle \phi } is the Euler function, η {\displaystyle \eta } is the Dedekind eta function, Δ ( z ) {\displaystyle \Delta (z)} is the modular discriminant, and q = e 2 π i z {\displaystyle q=e^{2\pi iz}} with I m ( z ) > 0 {\displaystyle \mathrm {Im} (z)>0} .

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