Hone, Andrew N.W. (2007) Sigma function solution of the initial value problem for Somos 5 sequences. Transactions of the American Mathematical Society, 359 (10). pp. 50195034. ISSN 00029947. (doi:10.1090/S0002994707042158) (KAR id:771)
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Official URL: http://dx.doi.org/10.1090/S0002994707042158 
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 

DOI/Identification number:  10.1090/S0002994707042158 
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:  Divisions > Division of Computing, Engineering and Mathematical Sciences > School of Mathematics, Statistics and Actuarial Science 
Depositing User:  Andrew Hone 
Date Deposited:  19 Dec 2007 18:28 UTC 
Last Modified:  16 Nov 2021 09:39 UTC 
Resource URI:  https://kar.kent.ac.uk/id/eprint/771 (The current URI for this page, for reference purposes) 
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