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Fermat Diophantine equations over function fields. (English) Zbl 1199.30200

Summary: We give a survey on some kinds of Diophantine equations over function fields. These results concern with the existence or non-existence of meromorphic(entire) solutions of the Fermat type functional equations by using the Nevanlinna’s theory.

MSC:

30D35 Value distribution of meromorphic functions of one complex variable, Nevanlinna theory
30D20 Entire functions of one complex variable (general theory)
11D41 Higher degree equations; Fermat’s equation
11R18 Cyclotomic extensions
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