Complex and p-adic branched functions and growth of entire functions

Abstract : Following a previous paper by Jacqueline Ojeda and the first author, here we examine the number of possible branched values and branched functions for certain p-adic and complex meromorphic functions where numerator and denominator have different kind of growth, either when the denominator is small comparatively to the numerator, or vice-versa, or (for p-adic functions) when the order or the type of growth of the numerator is different from this of the denominator: this implies that one is a small function comparatively to the other. Finally, if a complex meromorphic function f g admits four perfectly branched small functions, then T (r, f) and T (r, g) are close. If a p-adic meromorphic function f g admits four branched values, then f and g have close growth. We also show that, given a p-adic meromorphic function f , there exists at most one small function w such that f − w admits finitely many zeros and an entire function admits no such a small function.
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Contributor : Alain Escassut <>
Submitted on : Wednesday, November 28, 2018 - 11:14:57 AM
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Alain Escassut, Kamal Boussaf, Jacqueline Ojeda. Complex and p-adic branched functions and growth of entire functions. Bulletin of the Belgian Mathematical Society - Simon Stevin, Belgian Mathematical Society, 2015. ⟨hal-01922099⟩



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