Wieferich primes for Drinfeld modules
Résumé
The aim of this paper is to discuss the notion of Wieferich primes in the context of Drinfeld modules. Our main result is a surprising connection between the proprety of a monic irreducible polynomial p to be Wieferich and the p-adic valuation of special L-values of Drinfeld modules. This generalizes a theorem of Thakur for the Carlitz module.
We also study statistical distributions of Wieferich primes, proving in particular that a place of degree d is Wieferich with the expected probability q^d when we average over large enough sets of Drinfeld modules.
Domaines
Théorie des nombres [math.NT]| Origine | Fichiers produits par l'(les) auteur(s) |
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