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Elliptic Curves and Quadratic Recurrence Sequences

Elliptic Curves and Quadratic Recurrence Sequences 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. 2000 Mathematics Subject Classification 11B37 (primary), 33E05, 37J35 (secondary). http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Bulletin of the London Mathematical Society Wiley

Elliptic Curves and Quadratic Recurrence Sequences

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References (32)

Publisher
Wiley
Copyright
© London Mathematical Society
ISSN
0024-6093
eISSN
1469-2120
DOI
10.1112/S0024609304004163
Publisher site
See Article on Publisher Site

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. 2000 Mathematics Subject Classification 11B37 (primary), 33E05, 37J35 (secondary).

Journal

Bulletin of the London Mathematical SocietyWiley

Published: Apr 1, 2005

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