The Riemann Problem, Complete Integrability and Arithmetic Applications: Proceedings of a Seminar Held at the Institut des Hautes Etudes Scientifiques, Bures-sur Yvette, France, and at Columbia University, New York, U.S.A., 1979–1980

Introduction....Pages 1-11
Continuous exponents of spin correlation functions of inhomogeneous layered ising models....Pages 12-27
Introduction to holonomic quantum fields....Pages 28-36
Planar ising ferromagnet: correlation functions and the inverse scattering method....Pages 37-56
Infinite component σ-models and instanton solutions....Pages 57-70
Infinite component two-dimensional completely integrable systems of KdV type....Pages 71-84
The representation of an arbitrary, two-dimensional completely integrable system as the common action of two commuting one-dimensional Hamiltonian flows....Pages 85-94
Self-duality of Yang-Mills fields and of gravitational instantons....Pages 95-102
On proving the nonintegrability of a Hamiltonian system....Pages 103-122
Classical solutions in nonlinear Euclidean field theory and complete integrability....Pages 123-133
Hamiltonian structure of isospectral deformation equations. Elliptic curve case....Pages 134-146
Quantum Hamiltonians associated with finite-dimensional Lie algebras and factorized s-matrices....Pages 147-156
Classical and quantum operator nonlinear schrodinger equation. I....Pages 157-177
Trace identities for the Schröedinger operator and the WKB method....Pages 178-183
Zeta functions of the quartic (and homogeneous anharmonic) oscillators....Pages 184-208
On trace formula....Pages 209-214
Resolvent and trace identities in the one dimensional case....Pages 215-220
The devil's stair case transformation in incommensurate lattices....Pages 221-245
The convergence of padé approximants and their generalizations....Pages 246-257
Note on generalized jacobi polynomials....Pages 258-270
Multidimensional hermite interpolation and Padé approximation....Pages 271-298
Hermite-padé approximations to exponential functions and elementary estimates of the measure of irrationality of π....Pages 299-322
Criteria of algebraic independence of several numbers....Pages 323-368
Rational approximation for non-linear ordinary differential equations....Pages 369-373