A survey of Igusa's local zeta function (Q2800424)

In mathematics and in mathematical physics, the Igusa zeta function is related to a type of generating function, counting the number of solutions of an equation, modulo \(p\), and so on. The author gives a detailed investigation on the Igusa local zeta function and related subjects. The author discusses many conjectures related to this zeta function such as the Bernstein polynomials conjecture, the monodromy conjecture and others. By using the Igusa local zeta function and related conjectures, she shows how topological and motivic zeta functions are constructed. The author also presents Igusa's conjecture on exponential sums. Finally, the author studies various results, identities, remarks and observations on the Igusa's local zeta function and related functions.