The ``\(abc\)'' conjecture over function fields (Q1594773)

The authors formulate and prove an interesting result amounting to the \(abc\)-conjecture for entire functions over non-archimedean algebraically closed fields of characteristic zero (in the sense that when the entire functions are polynomials, then their result is Mason's \(abc\)-theorem over such fields). The argument consists substantially of an instructive application of the authors' value distribution theory [J. Contemp. Math. Anal., Armen. Acad. Sci. 32, No. 4, 45-80 (1997; Zbl 0946.30029)] for \(p\)-adic meromorphic functions.