On the Integrality of Somos 4 Sequences

Yıl 2019, Cilt: 12 Sayı: 1, 49 - 55, 24.03.2019

Betül Gezer

https://doi.org/10.18185/erzifbed.415008

Öz

In
this paper, it is shown that if (h_n) is a Somos 4 sequence
associated to an elliptic curve then each h_n 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.

Somos 4 Dizilerinin Tamsayılık Özelliği Üzerine

Öz

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.

Anahtar Kelimeler

Somos 4 sequences , elliptic curves

Kaynakça

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