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ELLIPTIC CURVES AND QUADRATIC RECURRENCE SEQUENCES

Published online by Cambridge University Press:  10 March 2005

A. N. W. HONE
A. N. W. HONE
Affiliation:
Institute of Mathematics, Statistics & Actuarial Science, University of Kent, Canterbury CT2 7NF, United [email protected]
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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.

Keywords

11B37 (primary)33E0537J35 (secondary)
Type
Papers
Information
Bulletin of the London Mathematical Society , Volume 37 , Issue 2 , March 2005 , pp. 161 - 171
Copyright
© The London Mathematical Society 2005

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