Tau function

In mathematics, Ramanujan's tau function is an arithmetic function which may defined in terms of the Delta form by the formal infinite product


 * $$q \prod_{n=1}^\infty \left(1-q^n\right)^{24} = \sum_n \tau(n) q^n .\,$$

Since Δ is a Hecke eigenform, the tau function is multiplicative, with formal Dirichlet series and Euler product


 * $$ \sum_n \tau(n) n^{-s} = \prod_p \left(1 - \tau(p) p^{-s} + p^{11-2s} \right)^{-1} .\,$$