Igusa's Theorem
Jun-Ichi Igusa (1974) showed that is a rational function in . The proof uses Heisuke Hironaka's theorem about the resolution of singularities. Later, an entirely different proof was given by Jan Denef using p-adic cell decomposition. Little is known, however, about explicit formulas. (There are some results about Igusa zeta functions of Fermat varieties.)
Read more about this topic: Igusa Zeta-function
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“To insure the adoration of a theorem for any length of time, faith is not enough, a police force is needed as well.”
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