Local zeta functions and Newton polyhedra
نویسندگان
چکیده
منابع مشابه
Local Zeta Functions Supported on Analytic Submanifolds and Newton Polyhedra
The local zeta functions (also called Igusa’s zeta functions) over p-adic fields are connected with the number of solutions of congruences and exponential sums mod pm. These zeta functions are defined as integrals over open and compact subsets with respect to the Haar measure. In this paper, we introduce new integrals defined over submanifolds, or more generally, over non-degenerate complete in...
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By using sheaf-theoretical methods such as constructible sheaves, we generalize the formula of Libgober-Sperber [17] concerning the zeta functions of monodromy at infinity of polynomial maps into various directions. In particular, some formulas for the zeta functions of global monodromy along the fibers of bifurcation points of polynomial maps will be obtained.
متن کاملMonodromy zeta functions at infinity , Newton polyhedra and constructible sheaves ∗
By using sheaf-theoretical methods such as constructible sheaves, we generalize the formula of Libgober-Sperber [15] concerning the zeta functions of monodromy at infinity of polynomial maps into various directions. In particular, some formulas for the zeta functions of global monodromy along the fibers of bifurcation points of polynomial maps will be obtained.
متن کاملZeta Functions for Analytic Mappings, Log-principalization of Ideals, and Newton Polyhedra
In this paper we provide a geometric description of the possible poles of the Igusa local zeta function ZΦ(s, f) associated to an analytic mapping f = (f1, . . . , fl) : U(⊆ K ) → K, and a locally constant function Φ, with support in U , in terms of a log-principalizaton of the K [x]−ideal If = (f1, . . . , fl). Typically our new method provides a much shorter list of possible poles compared wi...
متن کاملMonodromy Zeta-functions of Deformations and Newton Diagrams
For a one-parameter deformation of an analytic complex function germ of several variables, there is defined its monodromy zeta-function. We give a Varchenko type formula for this zeta-function if the deformation is non-degenerate with respect to its Newton diagram.
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ژورنال
عنوان ژورنال: Nagoya Mathematical Journal
سال: 2003
ISSN: 0027-7630,2152-6842
DOI: 10.1017/s0027763000008631