Critères d'irréductibilite des polynômes composés à coefficients dans un corps fini
Cycles of polynomials in algebraically closed fields of positive characteristic
Cyclotomic properties of the Rudin-Shapiro polynomials.
Détermination des fonctions entières irréductibles, suivant un module premier, dans le cas où le degré est égal au module.
Determination of a type of permutation trinomials over finite fields
Let . We find explicit conditions on a and b that are necessary and sufficient for f to be a permutation polynomial of . This result allows us to solve a related problem: Let (n ≥ 0, ) be the polynomial defined by the functional equation . We determine all n of the form , α > β ≥ 0, for which is a permutation polynomial of .
Dickson curves.
Dickson Polynomials that are Permutations
2000 Mathematics Subject Classification: 11T06, 13P10.A theorem of S.D. Cohen gives a characterization for Dickson polynomials of the second kind that permutes the elements of a finite field of cardinality the square of the characteristic. Here, a different proof is presented for this result.Research supported by the CERES program of the Ministry of Education, Research and Youth, contract nr. 39/2002.
Diophantine inequalities for the non-Archimedean line
Distinct Degree Factorizations in Additive arithmetical semigroups.
Elementary method in the theory of congruences for a prime modulus
Ensembles de polynômes irréductibles et théorèmes de densité
Équirépartition modulo dans un corps de séries formelles sur un corps fini
Equivalence classes of functions over a finite field
Equivalence classes of polynomials over finite fields
Equivalence classes of sets of functions over a finite field
Explicit constructions of extractors and expanders
Explicit formulas for strong Davenport pairs
Extension of semiclean rings
This paper aims at the study of the notions of periodic, UU and semiclean properties in various context of commutative rings such as trivial ring extensions, amalgamations and pullbacks. The results obtained provide new original classes of rings subject to various ring theoretic properties.
Factoring polynomials in finite fields: an application of Lang-Weil to a problem in graph theory.
Factorisation sur des polynômes de degré élevé à l’aide d’un monomorphisme