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We study the twisted local zeta function associated to a polynomial in twovariables with coefficients in a non-Archimedean local field of arbitrarycharacteristic. Under the hypothesis that the polynomial is arithmetically nondegenerate, we obtain an explicit list of candidates for the poles in terms ofgeometric data obtained from a family of arithmetic Newton polygons attached tothe polynomial. The notion of arithmetical non degeneracy due to Saia andZ\'u\~niga-Galindo is weaker than the usual notion of non degeneracy due toKouchnirenko. As an application we obtain asymptotic expansions for certainexponential sums attached to these polynomials.

Igusa's Local Zeta Functions and Exponential Sums for Arithmetically Non Degenerate Polynomials