In this article, we study local zeta functions attached to Laurent
polynomials over p-adic fields, which are non-degenerate with respect to their
Newton polytopes at infinity. As an application we obtain asymptotic expansions
for p-adic oscillatory integrals attached to Laurent polynomials. We show the
existence of two different asymptotic expansions for p-adic oscillatory
integrals, one when the absolute value of the parameter approaches infinity,
the other when the absolute value of the parameter approaches zero. These two
asymptotic expansions are controlled by the poles of twisted local zeta
functions of Igusa type.Comment: The condition on the critical set on the mapping f considered in
Section 2.5 of our article is not sufficient to assure the vanishing of the
twisted local zeta functions (for almost all the characters) as we assert in
Theorem 3.9. A new condition on the mapping f is provide
