Zeros of the derivative of a p-adic meromorphic function
Résumé
Let K be a complete algebraically closed field of characteristic 0 and let f be a transcen-dental meromorphic function in K. A conjecture suggests that f takes every values infinitely many times, what was proved when f has finitely many multiple poles. Here we can generalize the conclusion just by assuming that there exists positive constants c, d such that number of multiple poles inside the disk |x| ≤ r is less than cr d for all r ≥ 1. Applications are given to entire functions g in K such that g divides g, to links between residues and zeros of functions admitting primitives and finally to the p-adic Hayman conjecture in the cases that are not yet solved.
Domaines
Théorie des nombres [math.NT]
Origine : Fichiers produits par l'(les) auteur(s)
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