Displaying similar documents to “Canonical bases for subalgebras on two generators in the univariate polynomial ring.”

On the algebra of constants of polynomial derivations in two variables

Janusz Zieliński (2000)

Colloquium Mathematicae

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Let d be a k-derivation of k[x,y], where k is a field of characteristic zero. Denote by d ˜ the unique extension of d to k(x,y). We prove that if ker d ≠ k, then ker d ˜ = (ker d)0, where (ker d)0 is the field of fractions of ker d.

Non-zero constant Jacobian polynomial maps of ℂ ²

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.

Jung's type theorem for polynomial transformations of ℂ²

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 x m y n + terms of degree < m+n.

Multiplicity estimate for solutions of extended Ramanujan’s system

Evgeniy Zorin (2012)

Journal de Théorie des Nombres de Bordeaux

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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).