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The spectrum of difference operators and algebraic curves. (English) Zbl 0502.58032

##### MSC:
 37A30 Ergodic theorems, spectral theory, Markov operators 14H40 Jacobians, Prym varieties 47B39 Linear difference operators 37G99 Local and nonlocal bifurcation theory for dynamical systems 37J35 Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests 37K10 Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) 58C10 Holomorphic maps on manifolds 14K25 Theta functions and abelian varieties 32G20 Period matrices, variation of Hodge structure; degenerations 14C40 Riemann-Roch theorems 14H52 Elliptic curves 12H10 Difference algebra 14C35 Applications of methods of algebraic $$K$$-theory in algebraic geometry 18F20 Presheaves and sheaves, stacks, descent conditions (category-theoretic aspects) 14H15 Families, moduli of curves (analytic) 14C20 Divisors, linear systems, invertible sheaves
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