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Value-sharing and uniqueness problems for non-Archimedean differential polynomials in several variables. (English) Zbl 1388.30055

Summary: We consider differential polynomials of Fermat-Waring type, constructed using polynomials of Yi’s type for meromorphic functions in a non-Archimedean field. Similarly to the Hayman Conjecture, we prove that the considered differential polynomials assume all values. We establish also a uniqueness theorem for these differential polynomials.

MSC:

30G06 Non-Archimedean function theory
30D35 Value distribution of meromorphic functions of one complex variable, Nevanlinna theory
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