Definition
For a prime number p let K be a p-adic field, i.e., R the valuation ring and P the maximal ideal. For denotes the valuation of z, and for a uniformizing parameter π of R.
Furthermore let be a Schwartz–Bruhat function, i.e. a locally constant function with compact support and let be a character of .
In this situation one associates to a non-constant polynomial the Igusa zeta function
where and dx is Haar measure so normalized that has measure 1.
Read more about this topic: Igusa Zeta-function
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