Valuations of Somos 4 sequences and canonical local heights on elliptic curves

Abstract

AbstractSomos 4 sequences are sequences of numbers defined by a bilinear recurrence relation of order 4 and include elliptic divisibility sequences as a special case. In this paper, we describe valuations of Somos 4 sequences in terms of canonical local heights on the associated elliptic curves. We consider both Archimedean and non-Archimedean valuations. As applications, we study the asymptotic behaviour of valuations of Somos 4 sequences and obtain another proof of the integrality of certain Somos 4 sequences.