Kepler Sets of Second-Order Linear Recurrence Sequences Over ${\mathbb{Q}}_p$

Abstract

Let $(a_n{)}_{n=0}^{\infty }$ be a second-order linear recurrence sequence with constant coefficients over the field of $p$-adic numbers ${\mathbb{Q}}_p$. We study the set of limit points of the sequence of consecutive ratios $(a_{n+1}/a_n{)}_{n=0}^{\infty }$ in ${\mathbb{Q}}_p$.

to appear in the International Journal of Number Theory