Displaying similar documents to “On the Łojasiewicz exponent of the gradient of a polynomial function”

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.

Sharper ABC-based bounds for congruent polynomials

Daniel J. Bernstein (2005)

Journal de Théorie des Nombres de Bordeaux

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Agrawal, Kayal, and Saxena recently introduced a new method of proving that an integer is prime. The speed of the Agrawal-Kayal-Saxena method depends on proven lower bounds for the size of the multiplicative semigroup generated by several polynomials modulo another polynomial h . Voloch pointed out an application of the Stothers-Mason ABC theorem in this context: under mild assumptions, distinct polynomials A , B , C of degree at most 1 . 2 deg h - 0 . 2 deg rad A B C cannot all be congruent modulo h . This paper presents two...

On subfields of k ( x )

Victor Alexandru, Nicolae Popescu (1986)

Rendiconti del Seminario Matematico della Università di Padova

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