On the growth of linear recurrences in function fields

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 $|G_n|\ge {\left({\max }_{j=1,\dots ,t}|{\alpha }_j|\right)}^{n(1-\epsilon )}$ holds true.

8 pages

References in corpus (1)

• Perfect powers in polynomial power sums

Cited by in corpus (5)

• A Polynomial Variant of Diophantine Triples in Linear Recurrences
• On the growth of multi-recurrences
• Quantitative growth of linear recurrences
• On the size of a linear combination of two linear recurrence sequences over function fields
• Computing the Density of the Positivity Set for Linear Recurrence Sequences