Far Eastern Mathematical Journal

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The Somos-6 sequences of rank 3

Avdeeva M.O.

2018, issue 1, P. 3-8

Abstract

Nondegenerate Somos-4 sequences have rank 2. The rank of the product of two such sequences does not exceed 4, and then the Somos-2k sequences with k = 2, 3, 4 arise. In this paper we construct pairs of Comos-4 sequences such that them products are the Comos-6 sequences.

Keywords: Somos sequences, elliptic functions, addition theorems

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References

[1] A. N. W. Hone, “Elliptic curves and quadratic recurrence sequences”, Bulletin of the London Mathematical Society, 37:2, (2005), 161–171. [2] R. Shipsey, Elliptic Divisibility Sequences, PhD Thesis, Goldsmith’s University of London, 2000. [3] C. Swart, “Elliptic curves and related sequences”, PhD thesis, Royal Holloway and Bedford New College, University of London, 2003. [4] Y.N. Fedorov, A.N.W. Hone, “Sigma function solution of the general Somos-6 recurrence via hyperelleptic Prym varieties”, Journal of Integrable Systems, 1:1, (2016), 1–34. [5] M. Somos, “Problem 1470”, Crux Mathematicorum, 15, (1989), 208. [6] A.N.W. Hone, C.S. Swart, “Integrality and the Laurent phenomenon for Somos 4 and Somos 5 sequences”, Mathematical Proceedings of the Cabrige Philosophical Society, 145, (2008), 65–85. [7] M.O. Avdeeva, V.A. Bykovskij, “Giperjellipticheskie sistemy posledovatel'nostej i funkcij”, Dal'nevostochnyj matematicheskij zhurnal, 16:2, (2016), 115–122. [8] A.A. Illarionov, “Funkcional'noe uravnenie i sigma-funkcija Vejershtrassa”, Funkcional'nyj analiz i ego prilozhenija, 50:4, (2016), 43–54.

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