On the irreducibility of -quadrinomials.
On the Irreducibility of Polynomials Taking Small Values.
On the irreducibility of some polynomials in two variables
On the irreducibility of the generalized Laguerre polynomials
On the Lehmer constant of finite cyclic groups
On the number of irreducible polynomials with 0,1 coefficients
On the number of polynomials of bounded measure
On the number of terms of a composite polynomial
On the number of terms of a power of a polynomial
On the product ...(1-z...k).
On the reducibility type of trinomials
On the reduction of Kronecker's modular systems whose elements are functions of two and three variables.
On three questions concerning -polynomials
We answer three reducibility (or irreducibility) questions for -polynomials, those polynomials which have every coefficient either or . The first concerns whether a naturally occurring sequence of reducible polynomials is finite. The second is whether every nonempty finite subset of an infinite set of positive integers can be the set of positive exponents of a reducible -polynomial. The third is the analogous question for exponents of irreducible -polynomials.
Orthogonality and the maximum of Littlewood cosine polynomials
Parametrization of integral values of polynomials
We will recall a recent result about the classification of those polynomial in one variable with rational coefficients whose image over the integer is equal to the image of an integer coefficients polynomial in possibly many variables. These set is polynomially generated over the integers by a family of polynomials whose denominator is and they have a symmetry with respect to a particular axis.We will also give a description of the linear factors of the bivariate separated polynomial over a...
Patterns and periodicity in a family of resultants
Given a monic degree polynomial and a non-negative integer , we may form a new monic degree polynomial by raising each root of to the th power. We generalize a lemma of Dobrowolski to show that if and is prime then divides the resultant of and . We then consider the function . We show that for fixed and that this function is periodic in both and , and exhibits high levels of symmetry. Some discussion of its structure as a union of lattices is also given.
Polynomes à valeurs entières et propriété de Skolem.
Polynômes de Lagrange sur les entiers d'un corps quadratique imaginaire
L'objet de ce texte est de donner une estimation arithmétique des valeurs prises par les polynômes de Lagrange sur les entiers d'un corps quadratique imaginaire en des points de ce corps. Ces polynômes interviennent dans l'étude des fonctions entières arithmétiques et dans les minorations de formes linéaires de Logarithmes.
Polynomial Automorphisms Over Finite Fields
It is shown that the invertible polynomial maps over a finite field Fq , if looked at as bijections Fn,q −→ Fn,q , give all possible bijections in the case q = 2, or q = p^r where p > 2. In the case q = 2^r where r > 1 it is shown that the tame subgroup of the invertible polynomial maps gives only the even bijections, i.e. only half the bijections. As a consequence it is shown that a set S ⊂ Fn,q can be a zero set of a coordinate if and only if #S = q^(n−1).
Polynomial cycles in certain rings of rationals
It is shown that the methods established in [HKN3] can be effectively used to study polynomial cycles in certain rings. We shall consider the rings and shall describe polynomial cycles in the case when is either odd or twice a prime.