The Ramanujan tau function, studied by Ramanujan, is the function τ : N → Z {\displaystyle \tau :\mathbb {N} \rightarrow \mathbb {Z} } defined by the following identity: ∑ n ≥ 1 τ q n = q ∏ n ≥ 1 24 = q ϕ 24 = η 24 = Δ, {\displaystyle \sum _{n\geq 1}\tau q^{n}=q\prod _{n\geq 1}\left^{24}=q\phi ^{24}=\eta ^{24}=\Delta,} where q = exp with Im z > 0, ϕ {\displaystyle \phi } is the Euler function, η is the Dedekind eta function, and the function Δ is a holomorphic cusp form of weight 12 and level 1, known as the discriminant modular form. Wikipedia