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A generalized \(abc\)-conjecture over function fields. (English) Zbl 1007.11015

The authors suggest a generalised version of the \(abc\)-conjecture, in fact a sharpened \(a_0a_1\ldots a_k\)-conjecture, and provide an instructive proof of its analogue for non-Archimedean entire functions as well as of a sharpened generalisation of Mason’s theorem for polynomials.

MSC:

11D88 \(p\)-adic and power series fields
12J25 Non-Archimedean valued fields
30D35 Value distribution of meromorphic functions of one complex variable, Nevanlinna theory
30G06 Non-Archimedean function theory
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