Difference "abc" theorem for entire functions and Difference analogue of truncated version of Nevanlinna second main theorem
In this paper, we focus on the difference analogue of the Stothers-Mason theorem for entire functions of order less than 1, which can be seen as difference $abc$ theorem for entire functions. We also obtain the difference analogue of truncated version of Nevanlinna second main theorem which reveals that a subnormal meromorphic function $f(z)$ such that $Δf(z)\not\equiv 0$ cannot have too many points with long length in the complex plane. Both theorems depend on new definitions of the length of poles and zeros of a given meromorphic function in a domain. As for the application, we consider entire solutions of difference Fermat functional equations.
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