Displaying similar documents to “Poles of a local zeta function and Newton polygons”

On the Łojasiewicz exponent of the gradient of a holomorphic function

Andrzej Lenarcik (1998)

Banach Center Publications

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The Łojasiewicz exponent of the gradient of a convergent power series h(X,Y) with complex coefficients is the greatest lower bound of the set of λ > 0 such that the inequality | g r a d h ( x , y ) | ≥ c | ( x , y ) | λ holds near 0 ∈ C 2 for a certain c > 0. In the paper, we give an estimate of the Łojasiewicz exponent of grad h using information from the Newton diagram of h. We obtain the exact value of the exponent for non-degenerate series.

Characterization of jacobian Newton polygons of plane branches and new criteria of irreducibility

Evelia R. García Barroso, Janusz Gwoździewicz (2010)

Annales de l’institut Fourier

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In this paper we characterize, in two different ways, the Newton polygons which are jacobian Newton polygons of a plane branch. These characterizations give in particular combinatorial criteria of irreducibility for complex series in two variables and necessary conditions which a complex curve has to satisfy in order to be the discriminant of a complex plane branch.