Hone, Andrew N.W. (2005) Elliptic curves and quadratic recurrence sequences. Bulletin of the London Mathematical Society, 37 (Part 2). pp. 161-171. ISSN 0024-6093. (doi:10.1112/S0024609304004163) (The full text of this publication is not currently available from this repository. You may be able to access a copy if URLs are provided) (KAR id:682)
| The full text of this publication is not currently available from this repository. You may be able to access a copy if URLs are provided. | |
| Official URL: http://dx.doi.org/10.1112/S0024609304004163 |
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Abstract
The explicit solution of a general three-term bilinear recurrence relation of fourth order is constructed here in terms of the Weierstrass sigma function. The construction of the elliptic curve associated to the Somos 4 sequence is presented as an example. An interpretation via the theory of integrable systems is provided, leading to a conjecture relating certain higher-order recurrences with hyperelliptic curves of higher genus.
| Item Type: | Article |
|---|---|
| DOI/Identification number: | 10.1112/S0024609304004163 |
| Uncontrolled keywords: | BACKLUND-TRANSFORMATIONS; EQUATIONS; MAPS |
| Subjects: | Q Science > QA Mathematics (inc Computing science) |
| Institutional Unit: | Schools > School of Engineering, Mathematics and Physics > Mathematical Sciences |
| Former Institutional Unit: |
Divisions > Division of Computing, Engineering and Mathematical Sciences > School of Mathematics, Statistics and Actuarial Science
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| Depositing User: | Andrew Hone |
| Date Deposited: | 19 Dec 2007 18:25 UTC |
| Last Modified: | 20 May 2025 11:29 UTC |
| Resource URI: | https://kar.kent.ac.uk/id/eprint/682 (The current URI for this page, for reference purposes) |
University of Kent Author Information
Hone, Andrew N.W..
| Creator's ORCID: |
 https://orcid.org/0000-0001-9780-7369
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