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In a recent paper Z\'u\~niga-Galindo and the author begun the study of thelocal zeta functions for Laurent polynomials. In this work we continue thisstudy by giving a very explicit formula for the local zeta function associatedto a Laurent polynomial $f$ over a $p-$adic field, when $f$ is weaklynon-degenerate with respect to the Newton polytope of $f$ at infinity.

An Explicit Formula for the Local zeta Function of a Laurent Polynomial