1,234 research outputs found
Igusa's p-adic local zeta function associated to a polynomial mapping and a polynomial integration measure
For p prime, we give an explicit formula for Igusa's local zeta function
associated to a polynomial mapping f=(f_1,...,f_t): Q_p^n -> Q_p^t, with
f_1,...,f_t in Z_p[x_1,...,x_n], and an integration measure on Z_p^n of the
form |g(x)||dx|, with g another polynomial in Z_p[x_1,...,x_n]. We treat the
special cases of a single polynomial and a monomial ideal separately. The
formula is in terms of Newton polyhedra and will be valid for f and g
sufficiently non-degenerated over F_p with respect to their Newton polyhedra.
The formula is based on, and is a generalization of results of Denef -
Hoornaert, Howald et al., and Veys - Zuniga-Galindo.Comment: 20 pages, 5 figures, 2 table
Definable sets, motives and p-adic integrals
We associate canonical virtual motives to definable sets over a field of
characteristic zero. We use this construction to show that very general p-adic
integrals are canonically interpolated by motivic ones.Comment: 45 page
Motivic integration and the Grothendieck group of pseudo-finite fields
We survey our recent work on an extension of the theory of motivic
integration, called arithmetic motivic integration. We developed this theory to
understand how p-adic integrals of a very general type depend on p.Comment: 11 page
Character sums associated to finite Coxeter groups
We prove a character sum identity for Coxeter arrangements which is a finite
field analogue of Macdonald's conjecture proved by Opdam.Comment: 20 pages, to appear in Transactions of the A.M.
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