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SIGMA 3 (2007), 045, 17 pages math-ph/0703038
https://doi.org/10.3842/SIGMA.2007.045
Contribution to the Vadim Kuznetsov Memorial Issue
Spectral Curves of Operators with Elliptic Coefficients
J. Chris Eilbeck a, Victor Z. Enolski b and Emma Previato c
a) The Maxwell Institute and Department of
Mathematics, Heriot-Watt University, Edinburgh, UK EH14 4AS
b) Institute of Magnetism, 36 Vernadski Str., Kyiv-142, Ukraine
c) Department of Mathematics and Statistics, Boston University, Boston MA 02215-2411, USA
Received November 21, 2006, in final form February 16, 2007; Published online March 12, 2007
Abstract
A computer-algebra aided method is carried out, for
determining geometric objects associated to differential
operators that satisfy the elliptic ansatz. This results in
examples of Lamé curves with double reduction and in the
explicit reduction of the theta function of a Halphen curve.
Key words:
(equianharmonic) elliptic integrals; Lamé, Hermite, Halphen equation; theta function.
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