All a b c d e f g h i j k l m n o p q r s t u v w x y z Other

Previous Page 4 Next

Displaying 61 – 80 of 230

Showing per page

Determining Integer-Valued Polynomials From Their Image

Vadim Ponomarenko (2010)

Actes des rencontres du CIRM

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 Int ( ℤ ) 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 ℤ .

Effective Nullstellensatz for arbitrary ideals

János Kollár (1999)

Journal of the European Mathematical Society

Let f i be polynomials in n variables without a common zero. Hilbert’s Nullstellensatz says that there are polynomials g i such that ∑ g i f i = 1 . The effective versions of this result bound the degrees of the g i in terms of the degrees of the f j . The aim of this paper is to generalize this to the case when the f i are replaced by arbitrary ideals. Applications to the Bézout theorem, to Łojasiewicz–type inequalities and to deformation theory are also discussed.

Équations diophantiennes polynomiales à hautes multiplicités

Michel Langevin (2001)

Journal de théorie des nombres de Bordeaux

On montre comment écrire de grandes familles, avec de hautes multiplicités, de cas d’égalité A + B = C pour l’inégalité de Stothers-Mason (si A ( X ) , B ( X ) , C ( X ) sont des polynômes premiers entre eux, le nombre exact de racines du produit A B C dépasse de 1 le plus grand des degrés des composantes A , B , C ) . 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 ( a b c ) ou de M. Hall sont développés.

Extensions of the Bloch–Pólya theorem on the number of real zeros of polynomials

Tamás Erdélyi (2008)

Journal de Théorie des Nombres de Bordeaux

We prove that there are absolute constants c 1 > 0 and c 2 > 0 such that for every { a 0 , a 1 , ... , a n } ⊂ [ 1 , M ] , 1 ≤ M ≤ exp ( c 1 n 1 / 4 ) , there are b 0 , b 1 , ... , b n ∈ { - 1 , 0 , 1 } such that P ( z ) = ∑ j = 0 n b j a j z j has at least c 2 n 1 / 4 distinct sign changes in ( 0 , 1 ) . This improves and extends earlier results of Bloch and Pólya.

Finding the roots of polynomial equations: an algorithm with linear command.

Bernard Beauzamy (2000)

Revista Matemática Complutense

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.

Currently displaying 61 – 80 of 230