Short proofs of some results of algebraic independence in non-zero characteristic.

Federico Pellarin (1)

1 LMNO - Laboratoire de Mathématiques Nicolas Oresme

The aim of this note is to give short and almost elementary proofs of two theorems, by Papanikolas and Chang-Yu, on algebraic independence of Carlitz logarithms and values of Carlitz-Goss zeta function, modifying and generalising arguments of Denis which proved earlier special cases of these results. These proofs where sketched in the text [12] and this note is intended to accompany it, somewhat as an informal appendix, by giving full details to some few lines remarks.

Mots clés: Carlitz logarithms; Carlitz-Goss zeta function; algebraic independence

Domaines: Théorie des nombres [math.NT]

Federico Pellarin. Short proofs of some results of algebraic independence in non-zero characteristic.. 2007. ⟨hal-00146325⟩