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 Continuous exponents of spin correlation functions of inhomogeneous layered ising models to holonomic quantum fields Planar ising ferromagnet: correlation functions and the inverse scattering method Infinite component  models and instanton solutions Infinite component two dimensional completely integrable systems of KdV type The representation of an arbitrary two dimensional completely integrable system as the common action of two commuting one dimensional Hamiltonian flows Self duality of Yang Mills fields and of gravitational instantons On proving the nonintegrability of a Hamiltonian system Classical solutions in nonlinear Euclidean field theory and complete integrability Hamiltonian structure of isospectral deformation equations. Elliptic curve case Quantum Hamiltonians associated with finite dimensional Lie algebras and factorized s matrices Classical and quantum operator nonlinear schrodinger equation. I Trace identities for the Schröedinger operator and the WKB method Zeta functions of the quartic (and homogeneous anharmonic) oscillators On trace formula Resolvent and trace identities in the one dimensional case The devils stair case transformation in incommensurate lattices The convergence of padé approximants and their generalizations Note on generalized jacobi polynomials Multidimensional hermite interpolation and Padé approximation Hermite padé approximations to exponential functions and elementary estimates of the measure of irrationality of  Criteria of algebraic independence of several numbers Rational approximation for non linear ordinary differential equations.