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Journals / Erzincan Üniversitesi Fen Bilimleri Enstitüsü Dergisi / 2019 / Cilt: 12 - Sayı: 1

On the Integrality of Somos 4 Sequences

Somos 4 Dizilerinin Tamsayılık Özelliği Üzerine

Betül GEZER
Pages
49–55
Publication Date
2019-03-24
DOI
—
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

Also the general term of the Somos 4 sequence is given which satisfies a binary recurrence relation.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this paper, it is shown that if (hn) is a Somos 4 sequence associated to an elliptic curve then each hn can be expressed as elements of the ring R = ℤ[a1, a2, a3, a4, x, y, h–1±1, h0].
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Key Findings & Data:In particular, if h –1 = ±1, then the Somos 4 sequence consist entirely of integers for n ≥ 0.
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Conclusion & Impact:Also the general term of the Somos 4 sequence is given which satisfies a binary recurrence relation.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Somos 4 sequences · elliptic curves

Abstract

In this paper, it is shown that if (hn) is a Somos 4 sequence associated to an elliptic curve then each hn can be expressed as elements of the ring R = ℤ[a1, a2, a3, a4, x, y, h–1±1, h0]. In particular, if h –1 = ±1, then the Somos 4 sequence consist entirely of integers for n ≥ 0. Also the general term of the Somos 4 sequence is given which satisfies a binary recurrence relation.

Özet

Bu çalışmada, eğer (hn), bir eliptik eğri ile eşleşen bir Somos 4 dizisi ise her bir hn teriminin R = Z[a1, a2, a3, a4, x, y, h–1±1, h0] halkasının bir elemanı olarak ifade edilebileceği gösterilmiştir. Özel olarak n ≥ 0 için h –1 = ±1 ise Somos 4 dizisinin terimleri birer tamsayıdır. Üstelik bir ikili indirgeme bağıntısını gerçekleyen Somos 4 dizisinin genel terimi verilmiştir.

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Cite This Article

GEZER, B. (2019). On the Integrality of Somos 4 Sequences. Erzincan Üniversitesi Fen Bilimleri Enstitüsü Dergisi, Cilt: 12 - Sayı: 1, 49–55. https://ajindex.com/articles/234065

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