Quasi Ordinary Power Series and Their Zeta Functions is popular PDF and ePub book, written by Enrique Artal-Bartolo in 2005-10-05, it is a fantastic choice for those who relish reading online the Functions, Zeta genre. Let's immerse ourselves in this engaging Functions, Zeta book by exploring the summary and details provided below. Remember, Quasi Ordinary Power Series and Their Zeta Functions can be Read Online from any device for your convenience.
Quasi Ordinary Power Series and Their Zeta Functions Book PDF Summary
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.
Detail Book of Quasi Ordinary Power Series and Their Zeta Functions PDF
- Author : Enrique Artal-Bartolo
- Release : 05 October 2005
- Publisher : American Mathematical Soc.
- ISBN : 0821865633
- Genre : Functions, Zeta
- Total Page : 100 pages
- Language : English
- PDF File Size : 15,9 Mb
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