Formulae for the singularities at infinity of plane algebraic curves.
Gwoździewicz, Janusz, Płoski, Arkadiusz (2001)
Zeszyty Naukowe Uniwersytetu Jagiellońskiego. Universitatis Iagellonicae Acta Mathematica
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Gwoździewicz, Janusz, Płoski, Arkadiusz (2001)
Zeszyty Naukowe Uniwersytetu Jagiellońskiego. Universitatis Iagellonicae Acta Mathematica
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Bernard de Mathan (1992)
Acta Arithmetica
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In this paper, we study rational approximations for algebraic functions in characteristic p > 0. We obtain results for elements satisfying an equation of the type , where q is a power of p.
Nguyen Van Chau (1999)
Annales Polonici Mathematici
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We study the behavior at infinity of non-zero constant Jacobian polynomial maps f = (P,Q) in ℂ² by analyzing the influence of the Jacobian condition on the structure of Newton-Puiseux expansions of branches at infinity of level sets of the components. One of the results obtained states that the Jacobian conjecture in ℂ² is true if the Jacobian condition ensures that the restriction of Q to the curve P = 0 has only one pole.
Maria Frontczak, Przemysław Skibiński, Stanisław Spodzieja (1999)
Colloquium Mathematicae
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Janusz Gwoździewicz (1998)
Banach Center Publications
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Volker Ziegler (2007)
Journal de Théorie des Nombres de Bordeaux
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Thomas’ conjecture is, given monic polynomials with , then the Thue equation (over the rational integers) has only trivial solutions, provided with effective computable . We consider a function field analogue of Thomas’ conjecture in case of degree . Moreover we find a counterexample to Thomas’ conjecture for .
Jean-François Jaulent, Sebastian Pauli, Michael E. Pohst, Florence Soriano–Gafiuk (2008)
Journal de Théorie des Nombres de Bordeaux
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We present an algorithm for computing the 2-group of the positive divisor classes in case the number field has exceptional dyadic places. As an application, we compute the 2-rank of the wild kernel in .
Sławomir Kołodziej (1991)
Annales Polonici Mathematici
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We prove that among counterexamples to the Jacobian Conjecture, if there are any, we can find one of lowest degree, the coordinates of which have the form + terms of degree < m+n.