ON THE PRODUCT OF TRANSLATED DIVISION POLYNOMIALS AND SOMOS SEQUENCES

Gezer B., Bizim O.

FUNCTIONES ET APPROXIMATIO COMMENTARII MATHEMATICI, cilt.69, sa.1, ss.55-75, 2023 (ESCI) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 69 Sayı: 1
  • Basım Tarihi: 2023
  • Doi Numarası: 10.7169/facm/2038
  • Dergi Adı: FUNCTIONES ET APPROXIMATIO COMMENTARII MATHEMATICI
  • Derginin Tarandığı İndeksler: Emerging Sources Citation Index (ESCI), Scopus, Central & Eastern European Academic Source (CEEAS), MathSciNet, zbMATH
  • Sayfa Sayıları: ss.55-75
  • Anahtar Kelimeler: elliptic curves, translated division polynomials, Somos sequences, ELLIPTIC NETS, PERIODICITY
  • Bursa Uludağ Üniversitesi Adresli: Evet

Özet

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.