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december 2015 Complex and p-adic branched functions and growth of entire functions
Alain Escassut, Kamal Boussaf, Jacqueline Ojeda
Bull. Belg. Math. Soc. Simon Stevin 22(5): 781-796 (december 2015). DOI: 10.36045/bbms/1450389248

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 $\displaystyle{f\over g}$ admits four perfectly branched small functions, then $T(r,f)$ and $T(r,g)$ are close. If a p-adic meromorphic function $\displaystyle{f\over g}$ 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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Alain Escassut. Kamal Boussaf. Jacqueline Ojeda. "Complex and p-adic branched functions and growth of entire functions." Bull. Belg. Math. Soc. Simon Stevin 22 (5) 781 - 796, december 2015. https://doi.org/10.36045/bbms/1450389248

Information

Published: december 2015
First available in Project Euclid: 17 December 2015

zbMATH: 1329.30023
MathSciNet: MR3435082
Digital Object Identifier: 10.36045/bbms/1450389248

Subjects:
Primary: 12J25 , 30D35 , 30G06 , ‎46S10

Keywords: Branched values , Nevanlinna's Theory , Order and type of growth , p-adic meromorphic functions , Values distribution

Rights: Copyright © 2015 The Belgian Mathematical Society

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Vol.22 • No. 5 • december 2015
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