Sigma function solution of the initial value problem for Somos 5 sequences
数论
2007-05-23 v3
摘要
The Somos 5 sequences are a family of sequences defined by a fifth order bilinear recurrence relation with constant coefficients. For particular choices of coefficients and initial data, integer sequences arise. By making the connection with a second order nonlinear mapping with a first integral, we prove that the two subsequences of odd/even index terms each satisfy a Somos 4 (fourth order) recurrence. This leads directly to the explicit solution of the initial value problem for the Somos 5 sequences in terms of the Weierstrass sigma function for an associated elliptic curve.
引用
@article{arxiv.math/0501554,
title = {Sigma function solution of the initial value problem for Somos 5 sequences},
author = {Andrew Hone},
journal= {arXiv preprint arXiv:math/0501554},
year = {2007}
}
备注
More typos corrected, and extra Proposition 2.5 added. To appear in Trans. Amer. Math. Soc