Polynômes à valeurs entières ainsi que leurs dérivées en caractéristique p
Car-Pólya and Gel’fond’s theorems for
Fonctions à valeurs entières et module de Carlitz
Soient le module de Carlitz, un polynôme de et l’ensemble . Nous montrons qu’une fonction entière de type quadratique qui prend des valeurs entières sur , est polynomiale. De plus, la borne est optimale. Ceci est un analogue en caractéristique finie du théorème de Gel’fond-Pólya.
On the dynamics of in a local field
Let be a local field, and where denotes the characteristic of the residue field. We prove that the minimal subsets of the dynamical system are cycles and describe the cycles of this system.
Newton and Schinzel sequences in quadratic fields
We give the maximal length of a Newton or a Schinzel sequence in a quadratic extension of a global field. In the case of a number field, the maximal length of a Schinzel sequence is 1, except in seven particular cases, and the Newton sequences are also finite, except for at most finitely many cases, all real. We give the maximal length of these sequences in the special cases. We have similar results in the case of a quadratic extension of a function field , taking in account that the ring of integers...
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