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

In a recent paper Zúñiga-Galindo and the author begun the study of the local zeta functions for Laurent polynomials. In this work we continue this study by giving a very explicit formula for the local zeta function associated to a Laurent polynomial $f$ over a $p-$adic field, when $f$ is weakly non-degenerate with respect to the Newton polytope of $f$ at infinity.

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