High Quality Content by WIKIPEDIA articles! 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. Junichi Igusa showed that Z?(s,?) is a rational function in t = q ? s. 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.

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