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arXiv · 2006.11074

On the growth of linear recurrences in function fields

Clemens Fuchs·Sebastian Heintze
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Abstract

Let $ (G_n)_{n=0}^{\infty} $ be a non-degenerate linear recurrence sequence with power sum representation $ G_n = a_1(n) \alpha_1^n + \cdots + a_t(n) \alpha_t^n $. In this paper we will prove a function field analogue of the well known result that in the number field case, under some non-restrictive conditions, for $ n $ large enough the inequality $ \vert G_n\vert \geq \left( \max_{j=1,\ldots,t} \vert \alpha_j\vert \right)^{n(1-\varepsilon)} $ holds true.

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Clemens Fuchs, Sebastian Heintze. 2020-06-19. On the growth of linear recurrences in function fields. https://doi.org/10.1017/s0004972720001094

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