Far Eastern Mathematical Journal

To content of the issue


On integer Somos-8 and Somos-9 sequences


Monina M. D.

2015, issue 1, Ñ. 70-75


Abstract
The article offers a new method for constructing of integer sequences.

Keywords:
nonlinear sequences, quadratic recursive sequences, Weierstrass sigma-function, Somos sequences

Download the article (PDF-file)

References

[1] M. Somos, Problem 1470, Crux Mathematicorum 15 208, 1989.
[2] D. Gale, “Mathematical Entertainments: The Strange and Surprising Saga of the Somos Sequences”, Math. Intel., 13, 1991, 40–42.
[3] S. Fomin, A. Zelevinsky, “The Laurent Phenomenon”, Adv. Appl. Math., 28, 2002, 19–44.
[4] A. N. W. Hone, C. S. Swart, “Integrality and the Laurent phenomenon for Somos-4 and Somos-5 sequences”, Mathematical Proceedigs of the Cambridge Philosophical Society, 145 (2008), 65–85.
[5] A. N. W. Hone, “Elliptic curves and quadratic recurrence sequences”, Bull. Lond. Math. Soc., 37, 2005, 161–171.
[6] A. N. W. Hone, “Sigma function solution of the initial value problem for Somos-5 sequences”, Trans. Amer. Math. Soc. at press; math. NT/0501554, 2006.
[7] V. Bykovskii, “Elliptic systems of sequences and functions”, 2015, http://www.skoltech.ru/app/data/uploads/sites/29/2015/02/Skolkovo_Bykovskii.pdf.

To content of the issue