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Dergiler / Hacettepe Journal of Mathematics and Statistics / 2009 / Cilt: 38 - Sayı: 2

ELLIPTIC DIVISIBILITY SEQUENCES IN CERTAIN RANKS OVER FINITE FIELDS

B. GEZER
O. BİZİM
Sayfa
161–171
Yayın Tarihi
2009-02-01
DOI
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⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

After that, we give general terms of these sequences over the finite fields Fp (p > 3 is a prime) and then we determine elliptic curves and singular curves associated with them.

📌 3 Maddede Bu Makale

🎯
Amaç & Hipotez:We develop techniques first studied by Morgan Ward to characterize sequences which arise from elliptic curves and which contain a zero term.
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Temel Bulgular & Veri:We first define elliptic divisibility sequences over finite fields by noting that they are not the sequences which arise by reduction from integer sequences.
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Sonuç & Katkı:After that, we give general terms of these sequences over the finite fields Fp (p > 3 is a prime) and then we determine elliptic curves and singular curves associated with them.
🔬Tür:Araştırma Makalesi
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Elliptic divisibility sequences · Singular sequences · Elliptic curves

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 Fp (p > 3 is a prime) and then we determine elliptic curves and singular curves associated with them.

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Bu Makaleye Atıf Yap

GEZER, B., BİZİM, O. (2009). ELLIPTIC DIVISIBILITY SEQUENCES IN CERTAIN RANKS OVER FINITE FIELDS. Hacettepe Journal of Mathematics and Statistics, Cilt: 38 - Sayı: 2, 161–171. https://ajindex.com/articles/669755

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Kaynakça (10)

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  3. Everest, G. and Ward, T. Primes in divisibility sequences, Cubo Mat. Educ. 3, 245–259,
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  8. Tekcan, A., Gezer, B. and Bizim, O. Some relations on Lucas numbers and their sums, Advanced Studies in Comtemporary Mathematics 15 (2), 195–211, 2007.
  9. Ward, M. The law of repetition of primes in an elliptic divisibility sequences, Duke Math. J. 15, 941–946, 1948.
  10. Ward, M. Memoir on elliptic divisibility sequences, Amer. J. Math. 70, 31–74, 1948.