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Article Dans Une Revue Vietnam Journal of Mathematics Année : 2017

p-adic Nevanlinna Theory outside of a hole

Alain Escassut
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Ta Thi Hoai An
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Résumé

Let K be a complete ultrametric algebraically closed field of characteristic 0, take R > 0 and let D be the set {x ∈ K | |x| ≥ R}. Let M(D) be the field of meromorphic functions in D. We contruct a Nevanlinna Theory for M(D) and show many properties similar to those previously obtained with meromorphic functions in K or in an open disk. Functions have at most one Picard value and at most four branched values. The functions with finitely many poles in D have no Picard value and at most one branched value. URSCM and URSIM are similar to those in complex analysis. Fujimoto's way lets obtain polynomials of uniqueness for M(D) with a degree ≥ 5. Many algebraic curves admit no parametrization by functions of M(D). Motzkin Factors, known for analytic elements, here play an essential role.
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Dates et versions

hal-01918235 , version 1 (10-11-2018)

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  • HAL Id : hal-01918235 , version 1

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Alain Escassut, Ta Thi Hoai An. p-adic Nevanlinna Theory outside of a hole. Vietnam Journal of Mathematics, 2017. ⟨hal-01918235⟩
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