Cyclotomic polynomials with large coefficients
Détermination des diviseurs à coefficients commensurables, d’un degré donné, d’un polynôme entier en à coefficients commensurables
Determining Integer-Valued Polynomials From Their Image
This note summarizes a presentation made at the Third International Meeting on Integer Valued Polynomials and Problems in Commutative Algebra. All the work behind it is joint with Scott T. Chapman, and will appear in [2]. Let represent the ring of polynomials with rational coefficients which are integer-valued at integers. We determine criteria for two such polynomials to have the same image set on .
Die Primfaktorzerlegung der Werte der Kreisteilungspolynome.
Die Primfaktorzerlegung der Werte der Kreisteilungsprobleme. II.
Distribution of primes and a weighted energy problem.
Divisibilité des polynômes relativement aux puissances d'un nombre entier
Divisibility of integer polynomials and tilings of the integers
Easier Waring problems for commutative rings
Effective finiteness theorems for polynomials with given discriminant and integral elements with given discriminant over finitely domains.
Effective Nullstellensatz for arbitrary ideals
Let be polynomials in variables without a common zero. Hilbert’s Nullstellensatz says that there are polynomials such that . The effective versions of this result bound the degrees of the in terms of the degrees of the . The aim of this paper is to generalize this to the case when the are replaced by arbitrary ideals. Applications to the Bézout theorem, to Łojasiewicz–type inequalities and to deformation theory are also discussed.
Elliptic curves with bounded ranks in function field towers
Équations diophantiennes polynomiales à hautes multiplicités
On montre comment écrire de grandes familles, avec de hautes multiplicités, de cas d’égalité pour l’inégalité de Stothers-Mason (si sont des polynômes premiers entre eux, le nombre exact de racines du produit dépasse de le plus grand des degrés des composantes . On développera pour cela des techniques polynomiales itératives inspirées des décompositions de Dunford-Schwartz et de fonctions de Belyi. Des exemples d’application avec les conjectures ou de M. Hall sont développés.
Equations in one variable over function fields
Extensions of the Bloch–Pólya theorem on the number of real zeros of polynomials
We prove that there are absolute constants and such that for everythere aresuch thathas at least distinct sign changes in . This improves and extends earlier results of Bloch and Pólya.
Factoring Polynomials with Rational Coefficients.
Factorisation in fractional powers
Fifteen problems in number theory.
Finding integers k for which a given Diophantine equation has no solution in kth powers of integers
Finding the roots of polynomial equations: an algorithm with linear command.
We show how an old principle, due to Walsh (1922), can be used in order to construct an algorithm which finds the roots of polynomials with complex coefficients. This algorithm uses a linear command. From the very first step, the zero is located inside a disk, so several zeros can be searched at the same time.