Far Eastern Mathematical Journal

To content of the issue


About rank of Somos-6


Markova N.V.

2018, issue 1, Ñ. 71-74


Abstract
For theta functions from two variables follows from an addition formula that the rank of the sequence of Somos-6 does not surpass four. In work the example of the sequence of Somos-6 with a rank 4 is constructed.

Keywords:
Somos sequences, elliptic functions, addition theorems

Download the article (PDF-file)

References

[1] Hone A.N.W., “Elliptic curves and quadratic recurrence sequences”, Bulletin of the London Mathematical Society, 37:2, (2005), 161–171.
[2] Shipsey R., Elliptic Divisibility Sequences, PhD Thesis, Goldsmith’s University of London, 2000.
[3] Swart C., Elliptic curves and related sequences, PhD Thesis, Royal Holloway and Bedford New College, University of London, 2003.
[4] Fedorov Y.N., Hone A.N.W., “Sigma function solution of the general Somos-6 recurrence via hyperelleptic Prym varieties”, Journal of Integrable Systems, 1:1, (2016), 1–34, https://doi.org/10.1093/integr/xyw012.
[5] M. Somos, “Problem 1470”, Crux Mathematicorum, 15, (1989), 208.
[6] Gale D., “The strange and surprising saga of the Somos sequences”, Mathematical Intelligencer, 13:1, (1991), 40–42.
[7] M.O. Avdeeva, V.A. Bykovskij, “Giperjellipticheskie sistemy posledovatel'nostej i funkcij”, Dal'nevostochnyj matematicheskij zhurnal, 16:2, (2016), 115–122.

To content of the issue