FAR EASTERN BRANCH OF THE RUSSIAN ACADEMY OF SCIENCES
INSTITUTE OF APPLIED MATHEMATICS KHABAROVSK DIVISION
Far Eastern Mathematical Journal
On integer Somos-8 and Somos-9 sequences |
Monina M. D. |
2015, issue 1, P. 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. |