Geodesic
About rank of Somos-6
Dalʹnevostočnyj matematičeskij žurnal, Tome 18 (2018) no. 1, pp. 71-74 
N. V. Markova. About rank of Somos-6. Dalʹnevostočnyj matematičeskij žurnal, Tome 18 (2018) no. 1, pp. 71-74. http://geodesic.mathdoc.fr/item/DVMG_2018_18_1_a8/
@article{DVMG_2018_18_1_a8,
     author = {N. V. Markova},
     title = {About rank of {Somos-6}},
     journal = {Dalʹnevosto\v{c}nyj matemati\v{c}eskij \v{z}urnal},
     pages = {71--74},
     year = {2018},
     volume = {18},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DVMG_2018_18_1_a8/}
}
TY  - JOUR
AU  - N. V. Markova
TI  - About rank of Somos-6
JO  - Dalʹnevostočnyj matematičeskij žurnal
PY  - 2018
SP  - 71
EP  - 74
VL  - 18
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/DVMG_2018_18_1_a8/
LA  - ru
ID  - DVMG_2018_18_1_a8
ER  - 
%0 Journal Article
%A N. V. Markova
%T About rank of Somos-6
%J Dalʹnevostočnyj matematičeskij žurnal
%D 2018
%P 71-74
%V 18
%N 1
%U http://geodesic.mathdoc.fr/item/DVMG_2018_18_1_a8/
%G ru
%F DVMG_2018_18_1_a8

Voir la notice de l'article provenant de la source Math-Net.Ru

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.

[1] Hone A. N. W., “Elliptic curves and quadratic recurrence sequences”, Bulletin of the London Mathematical Society, 37:2 (2005), 161–171 | DOI | MR | Zbl

[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 | DOI

[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 | DOI | MR

[7] M.O. Avdeeva, V.A. Bykovskii, “Giperellipticheskie sistemy posledovatelnostei i funktsii”, Dalnevostochnyi matematicheskii zhurnal, 16:2 (2016), 115–122 | MR | Zbl