Sigma function solution of the initial valve problem for Somos 5 sequences

Hone, A.N.W. (2007) Sigma function solution of the initial valve problem for Somos 5 sequences. Transactions of the American Mathematical Society, 359 (10). pp. 5019-5034. ISSN 0002-9947. (Full text available)

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http://dx.doi.org/10.1090/S0002-9947-07-04215-8

Abstract

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.

Item Type: Article
Uncontrolled keywords: integer sequences; elliptic curves
Subjects: Q Science > QA Mathematics (inc Computing science)
Q Science > QA Mathematics (inc Computing science) > QA150 Algebra > QA241 Number theory
Divisions: Faculties > Science Technology and Medical Studies > School of Mathematics Statistics and Actuarial Science > Applied Mathematics
Faculties > Science Technology and Medical Studies > School of Mathematics Statistics and Actuarial Science
Depositing User: Judith Broom
Date Deposited: 19 Dec 2007 18:28
Last Modified: 16 Dec 2011 11:23
Resource URI: http://kar.kent.ac.uk/id/eprint/771 (The current URI for this page, for reference purposes)
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