On a decomposition of polynomials in several variables
One considers representation of a polynomial in several variables as the sum of values of univariate polynomials taken at linear combinations of the variables.
On a decomposition of polynomials in several variables, II
One considers representation of cubic polynomials in several variables as the sum of values of univariate polynomials taken at linear combinations of the variables.
On a galoisian approach to the splitting of separatrices
On a general difference Galois theory I
We know well difference Picard-Vessiot theory, Galois theory of linear difference equations. We propose a general Galois theory of difference equations that generalizes Picard-Vessiot theory. For every difference field extension of characteristic , we attach its Galois group, which is a group of coordinate transformation.
On a general difference Galois theory II
We apply the General Galois Theory of difference equations introduced in the first part to concrete examples. The General Galois Theory allows us to define a discrete dynamical system being infinitesimally solvable, which is a finer notion than being integrable. We determine all the infinitesimally solvable discrete dynamical systems on the compact Riemann surfaces.
On a polynomial conjecture of Pál Turán
On a problem of Aczél and Erdös concerning Hamel bases.
On a problem of Dvornicich and Zannier
On a question of Schinzel about the length and Mahler's measure of polynomials that have a zero on the unit circle
On a sequence of nonsolvable quintic polynomials.
On a Stratification Defined by Real Roots of Polynomials
2000 Mathematics Subject Classification: 12D10We prove smoothness of the strata and a transversality property of their tangent spaces.
On a Theorem of M. Deuring and I.R. Safarevic.
On a theorem of Ritt and related Diophantine problems.
On a universal axiomatization of the real closed fields
This paper presents a natural axiomatization of the real closed fields. It is universal and admits quantifier elimination.
On algebraic closures.
This is a description of some different approaches which have been taken to the problem of generalizing the algebraic closure of a field. Work surveyed is by Enoch and Hochster (commutative algebra), Raphael (categories and rings of quotients), Borho (the polynomial approach), and Carson (logic).Later work and applications are given.
On Algebraic Curves over Real Closed Fields.
On Algebraic Curves over Real Closed Fields. II.
On an iterated construction of irreducible polynomials over finite fields of even characteristic by Kyuregyan
We deal with the construction of sequences of irreducible polynomials with coefficients in finite fields of even characteristic. We rely upon a transformation used by Kyuregyan in 2002, which generalizes the -transform employed previously by Varshamov and Garakov (1969) as well as by Meyn (1990) for the synthesis of irreducible polynomials. While in the iterative procedure described by Kyuregyan the coefficients of the initial polynomial of the sequence have to satisfy certain hypotheses, in the...
On Apery's differential operator
On approximate roots of a polynomial.