Non-existence of meromorphic solutions of a Fermat type functional equation

In this paper, we will first establish a uniqueness theorem for meromorphic functions f 1 , f 2 , and f 3 that satisfy the functional equation f 1 +  f 2 +  f 3 = 1, and as applications, we give some results about the existence of meromorphic solutions of f n +  g n +  h n = 1 and two results relate...

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Bibliographic Details
Published in:Aequationes mathematicae 2008-09, Vol.76 (1-2), p.140-150
Main Authors: Yang, Lian-Zhong, Zhang, Ji-Long
Format: Article
Language:English
Subjects:
Analysis
Combinatorics
Mathematical problems
Mathematics
Mathematics and Statistics
Research Paper
Theorems
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Summary:In this paper, we will first establish a uniqueness theorem for meromorphic functions f 1 , f 2 , and f 3 that satisfy the functional equation f 1 +  f 2 +  f 3 = 1, and as applications, we give some results about the existence of meromorphic solutions of f n +  g n +  h n = 1 and two results related to a conjecture of R. Brück.
ISSN:0001-9054
1420-8903
DOI:10.1007/s00010-007-2913-7