ON THE PRODUCT OF TRANSLATED DIVISION POLYNOMIALS AND SOMOS SEQUENCES

Gezer B., Bizim O.

FUNCTIONES ET APPROXIMATIO COMMENTARII MATHEMATICI, vol.69, no.1, pp.55-75, 2023 (ESCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 69 Issue: 1
  • Publication Date: 2023
  • Doi Number: 10.7169/facm/2038
  • Journal Name: FUNCTIONES ET APPROXIMATIO COMMENTARII MATHEMATICI
  • Journal Indexes: Emerging Sources Citation Index (ESCI), Scopus, Central & Eastern European Academic Source (CEEAS), MathSciNet, zbMATH
  • Page Numbers: pp.55-75
  • Keywords: elliptic curves, translated division polynomials, Somos sequences, ELLIPTIC NETS, PERIODICITY
  • Bursa Uludag University Affiliated: Yes

Abstract

We consider the product sequences of the sequences (psi n(P)), (phi n(P)), and (omega n(P)) (n is an element of N) of values of the translated division polynomials of an elliptic curve E/K evaluated at a point P is an element of E(K)2. We prove that these sequences are purely periodic when K is a finite field. Then we use p-adic properties of these sequences to obtain p-adic convergence of product of the Somos 4 and Somos 5 sequences.