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arXiv · 2010.01896

On Pisot's $d$-th root conjecture for function fields and related GCD estimates

Ji Guo·Chia-Liang Sun·Julie Tzu-Yueh Wang
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Abstract

We propose a function-field analog of Pisot's $d$-th root conjecture on linear recurrences, and prove it under some "non-triviality" assumption. Besides a recent result of Pasten-Wang on B{\"u}chi's $d$-th power problem, our main tool, which is also developed in this paper, is a function-field analog of an GCD estimate in a recent work of Levin and Levin-Wang. As an easy corollary of such GCD estimate, we also obtain an asymptotic result.

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Ji Guo, Chia-Liang Sun, Julie Tzu-Yueh Wang. 2020-10-05. On Pisot's $d$-th root conjecture for function fields and related GCD estimates. https://arxiv.org/abs/2010.01896

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