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Article Dans Une Revue Bulletin des Sciences Mathématiques Année : 2012

Zeros of the derivative of a p-adic meromorphic function

Jean-Paul Bézivin
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Kamal Boussaf
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  • PersonId : 868552
Alain Escassut
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  • PersonId : 868596

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.
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Dates et versions

hal-01907050 , version 1 (28-10-2018)

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  • HAL Id : hal-01907050 , version 1

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Jean-Paul Bézivin, Kamal Boussaf, Alain Escassut. Zeros of the derivative of a p-adic meromorphic function. Bulletin des Sciences Mathématiques, 2012. ⟨hal-01907050⟩
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