Formulae for the singularities at infinity of plane algebraic curves.

Gwoździewicz, Janusz; Płoski, Arkadiusz

Displaying similar documents to “Formulae for the singularities at infinity of plane algebraic curves.”

Non-zero constant Jacobian polynomial maps of $ℂ ²$

Nguyen Van Chau (1999)

Annales Polonici Mathematici

Similarity:

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.

Approximation exponents for algebraic functions in positive characteristic

Bernard de Mathan (1992)

Acta Arithmetica

Similarity:

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 $α = (A α^{q} + B) / (C α^{q} + D)$ , where q is a power of p.

Salomon's Theorem for polynomials with several parameters

Maria Frontczak, Przemysław Skibiński, Stanisław Spodzieja (1999)

Colloquium Mathematicae

Similarity:

Growth at infinity of a polynomial with a compact zero set

Janusz Gwoździewicz (1998)

Banach Center Publications

Similarity:

Multiplicity estimate for solutions of extended Ramanujan’s system

Evgeniy Zorin (2012)

Journal de Théorie des Nombres de Bordeaux

Similarity:

We establish a new for solutions of a differential system extending Ramanujan’s classical differential relations. This result can be useful in the study of arithmetic properties of values of Riemann zeta function at odd positive integers (Nesterenko, 2011).

Thomas’ conjecture over function fields

Volker Ziegler (2007)

Journal de Théorie des Nombres de Bordeaux

Similarity:

Thomas’ conjecture is, given monic polynomials $p_{1},$ $..., p_{d} \in ℤ [a]$ with $0 < deg p_{1} < \dots < deg p_{d}$ , then the Thue equation (over the rational integers) $(X - p_{1} (a) Y) \dots (X - p_{d} (a) Y) + Y^{d} = 1$ has only trivial solutions, provided $a \geq a_{0}$ with effective computable $a_{0}$ . We consider a function field analogue of Thomas’ conjecture in case of degree $d = 3$ . Moreover we find a counterexample to Thomas’ conjecture for $d = 3$ .

Computation of 2-groups of positive classes of exceptional number fields

Jean-François Jaulent, Sebastian Pauli, Michael E. Pohst, Florence Soriano–Gafiuk (2008)

Journal de Théorie des Nombres de Bordeaux

Similarity:

We present an algorithm for computing the 2-group ${𝒞 ℓ}_{F}^{p o s}$ of the positive divisor classes in case the number field $F$ has exceptional dyadic places. As an application, we compute the 2-rank of the wild kernel $W K_{2} (F)$ in $K_{2} (F)$ .

Extension of polynomial mappings with a given Łojasiewicz exponent.

Karaś, Marek (2007)

Zeszyty Naukowe Uniwersytetu Jagiellońskiego. Universitatis Iagellonicae Acta Mathematica

Similarity: