Restrictions on meromorphic solutions of Fermat type equations

DOI10.1017/S001309152000005XzbMath1461.30075OpenAlexW3021215757MaRDI QIDQ4970546

Naofumi Kimura, Katsuya Ishizaki, Gary G. Gundersen

Publication date: 14 October 2020

Published in: Proceedings of the Edinburgh Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1017/s001309152000005x

zbMATH Keywords

polynomialsrational functionsNevanlinna theoryentire functionscomplex differential equationsmeromorphic functionsFermat-type functional equations

Mathematics Subject Classification ID

Value distribution of meromorphic functions of one complex variable, Nevanlinna theory (30D35) Entire functions of one complex variable (general theory) (30D20) Meromorphic functions of one complex variable (general theory) (30D30) Polynomials and rational functions of one complex variable (30C10)

Related Items (4)

Entire solutions of several quadratic binomial and trinomial partial differential-difference equations in \(\mathbb{C}^2\) ⋮ Transcendental solutions of Fermat-type functional equations in \(\mathbb{C}^n\) ⋮ Characterizations of entire solutions for the system of Fermat-type binomial and trinomial shift equations in \(\mathbb{C}^{n\#} \) ⋮ Difference radical in terms of shifting zero and applications to the Stothers-Mason theorem

Cites Work

• Nevanlinna theory and complex differential equations
• Waring's problem for the ring of polynomials
• A note on the functional equation \(f^{n}+g^{n}+h^{n}\)=1 and some complex differential equations
• Research questions on meromorphic functions and complex differential equations
• Entire and meromorphic solutions of the functional equation \(f^n+g^n+h^n=1\) and differential equations
• THE STRENGTH OF CARTAN'S VERSION OF NEVANLINNA THEORY
• On the equation 𝑓ⁿ+𝑔ⁿ=1
• On the functional equation \[ \sum_{i=0}^ p a_ i f_ i^{n_ i} = 1 \]
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