Hone, A.N.W. (2005) Elliptic curves and quadratic recurrence sequences. BULLETIN OF THE LONDON MATHEMATICAL SOCIETY, 37 (Part 2). pp. 161-171. ISSN 0024-6093.
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| Official URL http://dx.doi.org/10.1112/S0024609304004163 |
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 |
|---|---|
| Uncontrolled keywords: | BACKLUND-TRANSFORMATIONS; EQUATIONS; MAPS |
| Subjects: | Q Science > QA Mathematics (inc Computing science) |
| Divisions: | Faculties > Science Technology and Medical Studies > School of Mathematics Statistics and Actuarial Science |
| Depositing User: | Judith Broom |
| Date Deposited: | 19 Dec 2007 18:25 |
| Last Modified: | 16 Dec 2011 11:24 |
| Resource URI: | http://kar.kent.ac.uk/id/eprint/682 (The current URI for this page, for reference purposes) |
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