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Displaying similar documents to “Numerical invariants of 0-dimensional spaces and their Cartesian multiplication.”

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.

p -adic cycles

Bernard Dwork (1969)

Publications Mathématiques de l'IHÉS

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