Igusa zeta-function

In mathematics, an Igusa zeta function is a type of generating function, counting the number of solutions of an equation, modulo p, p², p³, and so on.

For a prime number p let K be a p-adic field, i.e. ${\displaystyle [K:\mathbb {Q} _{p}]<\infty }$, R the valuation ring and P the maximal ideal. For ${\displaystyle z\in K}$ we denote by ${\displaystyle \operatorname {ord} (z)}$ the valuation of z, ${\displaystyle \mid z\mid =q^{-\operatorname {ord} (z)}}$, and ${\displaystyle ac(z)=z\pi ^{-\operatorname {ord} (z)}}$ for a uniformizing parameter π of R.

...
Wikipedia