URSCM OR BI-URSCM FOR p-ADIC ANALYTIC OR MEROMORPHIC FUNCTIONS INSIDE A DISK

BOUTABAA, ABDELBAKI ; ESCASSUT, ALAIN

Glasgow mathematical journal, Tome 49 (2007) no. 1, pp. 121-126

Résumé

Let K be an algebraically closed field of characteristic zero, complete with respect to an ultrametric absolute value. In a previous paper, we had found URSCM of 7 points for the whole set of unbounded analytic functions inside an open disk. Here we show the existence of URSCM of 5 points for the same set of functions. We notice a characterization of BI-URSCM of 4 points (and infinity) for meromorphic functions in K and can find BI-URSCM for unbounded meromorphic functions with 9 points (and infinity). The method is based on the p-Adic Nevanlinna Second Main Theorem on 3 Small Functions applied to unbounded analytic and meromorphic functions inside an open disk and we show a more general result based upon the hypothesis of a finite symmetric difference on sets of zeros, counting multiplicities.

Détail

DOI : 10.1017/S0017089507003473

Mots-clés : 12J25, 46S10

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