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arXiv · 2011.10387

On a variant of Pillai's problem with transcendental numbers

Robert Tichy·Ingrid Vukusic·Daodao Yang·Volker Ziegler
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Abstract

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

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Robert Tichy, Ingrid Vukusic, Daodao Yang, Volker Ziegler. 2020-11-20. On a variant of Pillai's problem with transcendental numbers. https://doi.org/10.1007/s10474-022-01233-2

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