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

Published online by Cambridge University Press:  01 January 2007

ABDELBAKI BOUTABAA  and
ALAIN ESCASSUT
ABDELBAKI BOUTABAA
Affiliation:
Laboratoire de Mathématiques Pures, Université Blaise Pascal (Clermont-Ferrand), Les Cézeaux, 63177 Aubiere Cedex, France e-mail: Abdelbaki.Boutabaa@math.univ-bpclermont.frAlain.Escassut@math.univ-bpclermont.fr
ALAIN ESCASSUT
Affiliation:
Laboratoire de Mathématiques Pures, Université Blaise Pascal (Clermont-Ferrand), Les Cézeaux, 63177 Aubiere Cedex, France e-mail: Abdelbaki.Boutabaa@math.univ-bpclermont.frAlain.Escassut@math.univ-bpclermont.fr
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Abstract.

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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.

Keywords

12J2546S10
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 49 , Issue 1 , January 2007 , pp. 121 - 126
Copyright
Copyright © Glasgow Mathematical Journal Trust 2007

References

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