Decomposable polynomials in second order linear recurrence sequences

Abstract

We study elements of second order linear recurrence sequences $(G_n{)}_{n=0}^{\infty }$ of polynomials in $\mathbb{C}[x]$ which are decomposable, i.e. representable as $G_n=g\circ h$ for some $g,h\in \mathbb{C}[x]$ satisfying $\mathrm{deg}g,\mathrm{deg}h>1$. Under certain assumptions, and provided that $h$ is not of particular type, we show that $\mathrm{deg}g$ may be bounded by a constant independent of $n$, depending only on the sequence.

26 pages

References in corpus (2)

• On Ritt's polynomial decomposition theorems
• On factorizations of maps between curves