On the size of a linear combination of two linear recurrence sequences over function fields

Abstract

Let $G_n$ and $H_m$ be two non-degenerate linear recurrence sequences defined over a function field $F$ in one variable over $\mathbb{C}$, and let $\mu$ be a valuation on $F$. We prove that under suitable conditions there are effectively computable constants $c_1$ and $C^{\prime }$ such that the bound \begin{equation*} μ(G_n - H_m) \leq μ(G_n) + C' \end{equation*} holds for $\max \{n,m\}>c_1$.

10 pages

References in corpus (2)

• On the growth of linear recurrences in function fields
• A function field variant of Pillai's problem