Newton Polyhedra and Igusa's Local Zeta Function
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 کاملNewton Polyhedra (algebra and Geometry)
1.1. The ideology of general position. Suppose that the outcome of some natural process, such as a physical experiment, is the graph of a function of one variable over a closed interval of finite length. One feels that such a function ought to have only finitely many roots. Can this be proved rigorously? “Classical mathematics” answers this question with an univocal “no”: for any given closed s...
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ژورنال
عنوان ژورنال: Journal of Number Theory
سال: 2001
ISSN: 0022-314X
DOI: 10.1006/jnth.2000.2606