Applications of the \(p\)-adic Nevanlinna theory to functional equations.

DOI10.5802/aif.1771zbMath1063.30043OpenAlexW2318843856MaRDI QIDQ1572630

Abdelbaki Boutabaa, Alain Escassut

Publication date: 19 July 2000

Published in: Annales de l'Institut Fourier (Search for Journal in Brave)

Full work available at URL: http://www.numdam.org/item?id=AIF_2000__50_3_751_0

zbMATH Keywords

Picard-Berkovich's theorem

Mathematics Subject Classification ID

Functional analysis over fields other than (mathbb{R}) or (mathbb{C}) or the quaternions; non-Archimedean functional analysis (46S10) Value distribution of meromorphic functions of one complex variable, Nevanlinna theory (30D35) Non-Archimedean function theory (30G06) Functional equations and inequalities (39B99)

Related Items (7)

An analogue of Hilbert's 10th problem for fields of meromorphic functions over non-Archimedean valued fields ⋮ On the growth order of meromorphic solutions of some ultrametric \(q \)-difference equations ⋮ On some properties of ultrametric meromorphic solutions of Malmquist type ⋮ The functional equation \(P(f)=Q(g)\) in a \(p\)-adic field. ⋮ A note on \(p\)-adic linear differential equations ⋮ About the \(p\)-adic Yosida equation inside a disk ⋮ Applications of branched values to \(p\)-adic functional equations on analytic functions

Cites Work

• Theorie de Nevanlinna p-adique. (p-adic Nevanlinna theory)
• Urs, ursim, and non-urs for \(p\)-adic functions and polynomials
• Non-Archimedean analytic curves in Abelian varieties
• On uniqueness of \(p\)-adic entire functions
• Property \(f^{-1}(S)=g^{-1}(S)\) for entire and meromorphic \(P\)-adic functions
• URS AND URSIMS FOR P-ADIC MEROMORPHIC FUNCTIONS INSIDE A DISC
• On the equation 𝑓ⁿ+𝑔ⁿ=1
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