论文标题
Pillai问题的功能场变体
A function field variant of Pillai's problem
论文作者
论文摘要
在本文中，我们考虑了Pillai问题的变体，而不是功能字段$ f $在一个$ \ Mathbb {C} $上方的一个变量中。对于给定的简单线性复发序列$ g_n $和$ h_m $，定义在$ f $上并满足某些弱条件，我们将证明方程$ g_n -h_m = f $只有有限的许多解决方案$（n，m）\ in \ mathbb {n}^2 $，对于任何非零$ f $ in f $ in f $ in \ non -ZERE f $ in formed，in f $ in。此外，我们证明，在合适的假设下，只有许多有效的可计算$ f $有限的，其中一个以上表示$ g_n -h_m $。
In this paper, we consider a variant of Pillai's problem over function fields $ F $ in one variable over $ \mathbb{C} $. For given simple linear recurrence sequences $ G_n $ and $ H_m $, defined over $ F $ and satisfying some weak conditions, we will prove that the equation $ G_n - H_m = f $ has only finitely many solutions $ (n,m) \in \mathbb{N}^2 $ for any non-zero $ f \in F $, which can be effectively bounded. Furthermore, we prove that under suitable assumptions there are only finitely many effectively computable $ f $ with more than one representation of the form $ G_n - H_m $.
