The Somos-6 sequences of rank 3

M. O. Avdeeva

Khabarovsk Division of the Institute for Applied Mathematics, Far Eastern Branch, Russian Academy of Sciences

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.

Key words: Somos sequences, elliptic functions, addition theorems.

UDC: 517.52+512.742.72

MSC: Primary 11B37; Secondary 33E05

Received: 27.04.2018