Access the full text.
Sign up today, get DeepDyve free for 14 days.
N. Sloane (2003)
The On-Line Encyclopedia of Integer SequencesElectron. J. Comb., 1
A. Veselov, A. Shabat (1993)
Dressing chains and the spectral theory of the Schrödinger operatorFunctional Analysis and Its Applications, 27
Somos 6 sequence
(1965)
A course of modern analysis, 4th edn
G. Everest, T. Ward (2000)
The Canonical Height of an Algebraic Point on an Elliptic Curve
G. Everest, A. Poorten, I. Shparlinski, T. Ward (2003)
Recurrence Sequences, 104
M. Einsiedler, G. Everest, T. Ward (2001)
Primes in Elliptic Divisibility SequencesLms Journal of Computation and Mathematics, 4
The "bilinear" forum', and 'The Somos sequence site
A. Hone, V. Kuznetsov, O. Ragnisco (2000)
B?acklund transformations for the H'enon-Heiles and Garnier systems
S. Matsutani (2001)
Elliptic and hyperelliptic solutions of discrete Painlevé I and its extensions to higher order difference equationsPhysics Letters A, 300
I. Krichever, P. Wiegmann, A. Zabrodin (1998)
Elliptic Solutions to Difference Non-Linear Equations and Related Many-Body ProblemsCommunications in Mathematical Physics, 193
V. Arnold (1974)
Mathematical Methods of Classical Mechanics
Yuri Fedorov (2002)
Bäcklund Transformations on Coadjoint Orbits of the Loop AlgebraJournal of Nonlinear Mathematical Physics, 9
R. Hirota (1971)
Exact solution of the Korteweg-deVries equation for multiple collision of solitons
V. Bukhshtaber, I. Krichever (1993)
Vector addition theorems and Baker-Akhiezer functionsTheoretical and Mathematical Physics, 94
(1997)
on the crossroad, Amer
(2000)
an integrable discretization’, Internat
M. Ward (1948)
The law of repetition of primes in an elliptic divisibility sequenceDuke Mathematical Journal, 15
A. Hone, V. Kuznetsov, O. Ragnisco (1999)
Backlund transformations for many-body systems related to KdVJournal of Physics A, 32
Y. Ohta, J. Satsuma, D. Takahashi, T. Tokihiro (1988)
An Elementary Introduction to Sato TheoryProgress of Theoretical Physics Supplement, 94
A. Hone (1999)
Exact discretization of the Ermakov–Pinney equationPhysics Letters A, 263
R. Miranda (1995)
Algebraic Curves and Riemann Surfaces
Victor Snaith (2000)
HEIGHTS OF POLYNOMIALS AND ENTROPY IN ALGEBRAIC DYNAMICS (Universitext) By G RAHAM E VEREST and T HOMAS W ARD : 212 pp., £35.00, ISBN 1 85233 125 9 (Springer, 1999).Bulletin of The London Mathematical Society, 32
B. Dubrovin, V. Matveev, S. Novikov (1976)
NON-LINEAR EQUATIONS OF KORTEWEG-DE VRIES TYPE, FINITE-ZONE LINEAR OPERATORS, AND ABELIAN VARIETIESRussian Mathematical Surveys, 31
R. Amayo, I. Stewart (1974)
Infinite-dimensional Lie algebras
Christine Swart (2003)
Elliptic curves and related sequences
Y. Suris (1999)
The Motion of a Rigid Body in a Quadratic Potential: An Integrable DiscretizationInternational Mathematics Research Notices, 2000
R. Robinson (1992)
Periodicity of Somos sequences, 116
V. Buchstaber, S. Novikov (1997)
Solitons, Geometry, and Topology: On the Crossroad, 179
M. Bruschi, O. Ragnisco, P. Santini, G. Tu (1991)
Integrable symplectic mapsPhysica D: Nonlinear Phenomena, 49
M. Ward (1948)
Memoir on Elliptic Divisibility SequencesAmerican Journal of Mathematics, 70
A. Fordy, G. Quispel, J. Roberts, C. Thompson (1991)
Integrable mapsRussian Mathematical Surveys, 46
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).
Bulletin of the London Mathematical Society – Wiley
Published: Apr 1, 2005
Read and print from thousands of top scholarly journals.
Already have an account? Log in
Bookmark this article. You can see your Bookmarks on your DeepDyve Library.
To save an article, log in first, or sign up for a DeepDyve account if you don’t already have one.
Copy and paste the desired citation format or use the link below to download a file formatted for EndNote
Access the full text.
Sign up today, get DeepDyve free for 14 days.
All DeepDyve websites use cookies to improve your online experience. They were placed on your computer when you launched this website. You can change your cookie settings through your browser.