Sigma function solution of the initial value problem for Somos 5 sequences
| dc.creator | Hone, Andrew | |
| dc.date | 2005-01-31 | |
| dc.date | 2006-01-30 | |
| dc.date.accessioned | 2026-07-07T06:39:22Z | |
| dc.date.available | 2026-07-07T06:39:22Z | |
| dc.description | 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. | |
| dc.description | More typos corrected, and extra Proposition 2.5 added. To appear in Trans. Amer. Math. Soc | |
| dc.identifier | https://arxiv.org/abs/math/0501554 | |
| dc.identifier | http://arxiv.org/abs/math/0501554 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/101052 | |
| dc.subject | Number Theory | |
| dc.subject | 11B37, 33E05, 37J35 | |
| dc.title | Sigma function solution of the initial value problem for Somos 5 sequences | |
| dc.type | text |