On a variant of Pillai's problem with transcendental numbers

In this paper, we study the asymptotic behaviour of the number of solutions $(m, n)\in \mathbb{N}^2$ to the inequality $| α^n - β^m | \leq x$ when $x$ tends to infinity. Here $α, β$ are given multiplicatively independent complex numbers with $|α| > 1$ and $|β|>1$.

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