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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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.
|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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