论文标题
在PISOT的$ d $ - 功能字段和相关GCD估计的根本猜想上
On Pisot's $d$-th root conjecture for function fields and related GCD estimates
论文作者
论文摘要
我们在线性复发上提出了PISOT的$ d $ TH root猜想的功能场类似物，并在某些“非平凡性”假设下证明了它。除了最近在B {ü} Chi的$ d $ The Power问题上的Pasten-wang的结果外，我们的主要工具也在本文中开发，它是Levin和Levin-Wang的最新作品中GCD估算的功能场类似物。作为这种GCD估计值的简单推论，我们还获得了渐近结果。
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{ü}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.
