Zeroes of the derivative of a p-adic meromorphic function and applications
Résumé
Let K be an algebraically closed field of characteristic 0, complete with respect to an ultrametric absolute value. We show that if the Wronskian of two entire functions in K is a polynomial, then both functions are polynomials. As a consequence, if a meromorphic function f on all K is transcendental and has finitely many multiple poles, then f takes all values in K infinitely many times. We then study applications to a meromorphic function f such that f + bf 2 has finitely many zeroes, a problem linked to the Hayman conjecture on a p-adic field.
Domaines
Théorie des nombres [math.NT]
Origine : Fichiers produits par l'(les) auteur(s)
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