  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.
