Let $ (G_n)_{n=0}^{\infty } $ be a nondegenerate linear recurrence sequence whose power sum representation is given by $ G_n = a_1(n) \alpha _1^n + \cdots + a_t(n) \alpha _t^n $ . We prove a function field analogue of the well-known result in the number field case that, under some nonrestrictive conditions, $ |{G_n}| \geq ( \max _{j=1,\ldots ,t} |{\alpha _j}| )^{n(1-\varepsilon )} $ for $ n $ large enough.

中文翻译：

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关于函数领域中线性递归的增长

让 $ (G_n)_{n=0}^{\infty } $ 是一个非退化线性递归序列，其幂和表示由下式给出 $ G_n = a_1(n) \alpha _1^n + \cdots + a_t(n) \alpha _t^n $ . 我们证明了数域情况下众所周知的结果的函数域模拟，在一些非限制条件下， $ |{G_n}| \geq ( \max _{j=1,\ldots ,t} |{\alpha _j}| )^{n(1-\varepsilon )} $ 为了 $ n $ 足够大。