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Integrable equations, addition theorems, and the Riemann-Schottky problem. (English) Zbl 1134.14306
Russ. Math. Surv. 61, No. 1, 19-78 (2006); translation from Usp. Mat. Nauk 61, No. 1, 25-84 (2006).

MSC:
14H42 Theta functions and curves; Schottky problem
14H70 Relationships between algebraic curves and integrable systems
37K10 Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.)
37K20 Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with algebraic geometry, complex analysis, and special functions
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