ELLIPTIC DIVISIBILITY SEQUENCES IN CERTAIN RANKS OVER FINITE FIELDS

Gezer B., Bizim O.

HACETTEPE JOURNAL OF MATHEMATICS AND STATISTICS, vol.38, no.2, pp.161-171, 2009 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 38 Issue: 2
  • Publication Date: 2009
  • Journal Name: HACETTEPE JOURNAL OF MATHEMATICS AND STATISTICS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, TR DİZİN (ULAKBİM)
  • Page Numbers: pp.161-171
  • Bursa Uludag University Affiliated: Yes

Abstract

We develop techniques first studied by Morgan Ward to characterize sequences which arise from elliptic curves and which contain a zero term. We first define elliptic divisibility sequences over finite fields by noting that they are not the sequences which arise by reduction from integer sequences. After that, we give general terms of these sequences over the finite fields F(p) (p > 3 is a prime) and then we determine elliptic curves and singular curves associated with them.