Quasi-Ordinary Power Series and Their Zeta Functions

Quasi-Ordinary Power Series and Their Zeta Functions

4.11 - 1251 ratings - Source

The main objective of this paper is to prove the monodromy conjecture for the local Igusa zeta function of a quasi-ordinary polynomial of arbitrary dimension defined over a number field. In order to do it, we compute the local Denef-Loeser motivic zeta function $Z_{\text{DL}}(h, T)$ of a quasi-ordinary power series $h$ of arbitrary dimension over an algebraically closed field of characteristic zero from its characteristic exponents without using embedded resolution of singularities. This allows us to effectively represent $Z_{\text{DL}}(h, T)=P(T)/Q(T)$ such that almost all the candidate poles given by $Q(T)$ are poles. Anyway, these candidate poles give eigenvalues of the monodromy action on the complex $R\psi_h$ of nearby cycles on $h^{-1}(0).$ In particular we prove in this case the monodromy conjecture made by Denef-Loeser for the local motivic zeta function and the local topological zeta function. As a consequence, if $h$ is a quasi-ordinary polynomial defined over a number field we prove the Igusa monodromy conjecture for its local Igusa zeta function.Let 71, ..., 7r be the compact edges of the Newton diagram of h; for each q a€” 1, . . . , r, we have denoted by v(q) the number of non-zero distinct roots of h^q . Each one of these roots defines a Newton map and let hqj j = 1, . . . , v(q), be theanbsp;...

Title:Quasi-Ordinary Power Series and Their Zeta Functions
Author: Enrique Artal-Bartolo
Publisher:American Mathematical Soc. - 2005-10-05

You must register with us as either a Registered User before you can Download this Book. You'll be greeted by a simple sign-up page.

Once you have finished the sign-up process, you will be redirected to your download Book page.

How it works:
  • 1. Register a free 1 month Trial Account.
  • 2. Download as many books as you like (Personal use)
  • 3. Cancel the membership at any time if not satisfied.

Click button below to register and download Ebook
Privacy Policy | Contact | DMCA