Abstract
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.
Moments and distribution of values of $L$-functions
over function fields inside the critical strip
