Igusa Zeta-Function

Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. 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.