A way of Reducing the Factorization Problem in Z[x] to the Factorization Problem in Z
Abschätzungen ganzzahliger Polynome auf dem Intervall [0, 1].
Addendum to the paper: "On the number of terms of a composite polynomial" (Acta Arith. 127 (2007), 157-167)
Addendum to the papers "On polynomials taking small values at integral arguments I, II" (Acta Arith. 42 (1983), 189-196; ibid. 106 (2003), 115-121)
An Arithmetic Characterization of the Rational Homotopy Groups of Certain Spaces.
An effective procedure for minimal bases of ideals in Z[x]
We give an effective procedure to find minimal bases for ideals of the ring of polynomials over the integers.
An Egyptian algorithm for polynomials.
An explicit formula for the Mahler measure of a family of -variable polynomials
An explicit formula for the Mahler measure of the -variable Laurent polynomial is given, in terms of dilogarithms and trilogarithms.
An extension of a result of C. J. Smyth to polynomials in several variables
An irreducibility criterion for composition of polynomials.
An irreducibility criterion for polynomials in several variables
Anneaux de Fatou
Approximate polynomial GCD
The computation of polynomial greatest common divisor (GCD) ranks among basic algebraic problems with many applications, for example, in image processing and control theory. The problem of the GCD computing of two exact polynomials is well defined and can be solved symbolically, for example, by the oldest and commonly used Euclid’s algorithm. However, this is an ill-posed problem, particularly when some unknown noise is applied to the polynomial coefficients. Hence, new methods for the GCD computation...
Approximation d'un nombre p-adique par des nombres algebriques
Asymptotic distribution and symmetric means of algebraic numbers
Schur introduced the problem on the smallest limit point for the arithmetic means of totally positive conjugate algebraic integers. This area was developed further by Siegel, Smyth and others. We consider several generalizations of the problem that include questions on the smallest limit points of symmetric means. The key tool used in the study is the asymptotic distribution of algebraic numbers understood via the weak* limits of their counting measures. We establish interesting properties of the...
Autour d'un théorème de Stein.
Auxiliary polynomials for some problems regarding Mahler's measure
Bases for integer-valued polynomials in a Galois field
Bemerkung uber zwei Satze von Jakowkin
Block Factorization of Hankel Matrices and Euclidean Algorithm
It is shown that a real Hankel matrix admits an approximate block diagonalization in which the successive transformation matrices are upper triangular Toeplitz matrices. The structure of this factorization was first fully discussed in [1]. This approach is extended to obtain the quotients and the remainders appearing in the Euclidean algorithm applied to two polynomials u(x) and v(x) of degree n and m, respectively, whith m < ...